Here's my recollection of Crosby's career so far as well as some (mostly my) contemporaneous views:
(for TL;DR version, skip to end)
(NOTE: When grading playoff opposition, I'm primarily doing so against other playoff teams, not league-wide... and doing so on the basis of their overall strength and their defensive strength).
2006- 6th in scoring as a rookie... quite impressive, although perhaps a bit overshadowed by Ovechkin's thirds in points and (tie) goals.
2007- Wins the Ross... perhaps the hype is justified?
2008- Was competing for the Ross until injured... had a good playoff run, although one thing that struck me was how Jagr at age 36 appeared clearly the more impactful player in the playoff series vs. Crosby & Malkin. Not sure if it was then Jagr that called him out on the ice for basically being a whiny diver, but I know it was echoed by others (including Selanne) at various times.
2009- 3rd in scoring, behind both Malkin & Ovechkin, in what was the only season where all three were healthy and at/near peaks. While it was a fine season by Crosby, it was illustrative that his peak was never demonstrated to be above that of Ovechkin or Malkin. He won the great showdown with his rival in the playoffs, but each star performed well, and let's remember the Caps were a below average team defensively (league-wide, let alone among playoff teams). Then the Pens won their one Cup against a memorable team in the Crosby/Malkin era. This was also memorable for the series being moved up about a week, while the Wings' Datsyuk & Lidstrom were nursing injuries... and for the Pens, down 2 games to zero and trailing in game 3, having a blatant penalty for too many men missed/ignored while they controlled the puck in the offensive zone for a long stretch. If that clear, non-subjective penalty was called, do the Pens win that game? If they lose that game, do they come back from 3-0 vs. Detroit? The only spark the Pens had shown in the series to that point was Malkin throwing punches after game 2 ended... which also failed to result in any sort of infraction. Despite having 3 points in 7 games and being a (-3) vs. Detroit, and being outscored by 5 points by Malkin during the playoffs, many called for Crosby to get the Conn Smythe... a foreshadowing of the future.
2010- Tied for second in scoring with Ovechkin, behind Henrik Sedin. The only reason Ovechkin lost to Henrik and tied Crosby was that he missed 10 games (4 to injury, 2 each for two separate suspensions, and I believe 2 for his grandmother's passing?). After sailing through the first round, Crosby had 5 points and was (-2) in a 7 game series loss to a below average Habs team. He scored a tap-in on Canadian home ice vs. an underdog USA squad to win the gold. I understand the significance of this to Canadians thirsty for another gold, but it has little bearing on my evaluation of Crosby as a player.
2011- He got off to blazing hot start in the first half of the season. It wasn't long after Big Phil began a thread on HFB titled something like "Is Crosby the Best Player Since Mario?" that he got concussed while skating into his opponent as he completed skating a lazy circle in the defensive zone and was about to spectate the action up ice. So began the what-ifs, the could haves, & the would haves. At some point later I did study of best half-seasons since ~'94 and Crosby's 41 games of 2010-11 were not near the very top, even among players not named Mario, although still one of the best (top 10?).
2012- He puts up an excellent ppg avg. in only 22 games. Remember, he had 101 games off plus the previous playoffs, and is playing against players that have been grinding for ~60 games already. Some would say it was a disadvantage due to rust. I would say it was more of an advantage to be well-rested against tiring players, and all-time greats tend to shake off the rust during training. The Pens lose in the first round to Jagr and the Flyers in what was nothing less than a sh** show featuring a complete meltdown by the Pens, as they stooped to perhaps even below the Flyers' level of goonery, highlighted by Giroux's clean hit on Crosby late in the series, which pretty well sent the message that any comeback attempt would be futile.
2013- Another hot start for Crosby in the first 36 games, before his unfortunate injury. I know the injury is considered fluky, and not without reason, but a couple of things to remember: It was only 36 games into the season, so still very early by full-season standards. If you're gonna play "the world's best grinder" type of game at times, you're going to take more hits, sticks, and pucks than you otherwise would. Crosby had 6 points in 5 games against a Senators team that was defensively strong, although not so much overall. Crosby and the Pens were completely shut down offensively and absolutely clobbered in a sweep by the Bruins.
2014- Crosby wins his second Ross and dominates his competition. There's no denying it was a great year for Crosby, but his winning margin in the scoring race is frequently cited, while his relatively weak top-end competition is not. The six players immediately behind him combined for three other top 5 finishes in their careers: Perry was 3rd in 2011, and Giroux was 3rd in 2012 and 2nd in 2018. Crosby had a mediocre or worse series (6 in 6, -2) vs. Columbus, then a poor series (3 in 7, -2) as the Rangers came back from down 3-1 to win the series. At this point, several disappointing playoff series (some facepalm worthy) be damned (ignored), Crosby was back and according to HFB History consensus, as long as he could stay healthy (which I admittedly doubted at the time, and not without good reason, I think most would admit) he was about to reel off multiple consecutive Ross wins. With Ovechkin long past and far, far from his peak years... Malkin injured most years... and Crosby about to turn 27... this didn't seem so far-fetched. I was one of the few that cautioned "not so fast," that his was the first full season he had played since 2010 and since he was quite unusually rested (having only played 99 games +4 playoff rounds in 3 previous years), so it would be more reasonable to take a "wait and see" approach about his first back-to-back full seasons in a long while.
2015- I know he had the mumps for a bit and missed a few games, but I think it would take much more than that for some of the players he's competing with for #5 to finish third at age 27 behind Benn & Tavares. Remember, everybody and their brothers were predicting he would steamroll the competition for years to come... and Jamie Benn scores 87 points to take the Ross, while Crosby was third in 77 games. Nothing wrong with losing to a strong Rangers team in playoffs though.
2016- Sure, Kane's excellent, but Crosby at age 28 is outscored by 21 points by him? He's also outscored by Benn (again!) and within 3 points are a d-man (Karlsson) and an age 36 Thornton. This isn't exactly what I (and I assume others) mean by dominance. Here's where the narrative shifts, and somehow it's not important that Crosby is nowhere near dominant at ages 27-28, as now he's playing passable defense (rather than run and gun), as you'd expect of most centers, and the spin becomes all about team success: 2 points and (-3) in 6 games vs. hapless Caps?... "he shut down Ovechkin" (although he was outscored by him)... 5 points in 7 games (even) vs. Tampa?... well he did have one of his few memorable playoff goals in OT, but not at all dominant... 4 points, all assists, and even in 6 games vs. Sharks? meh. So he ends playoffs with 6 goals (tied with three others for third on team, 4 behind Kessel), 19 points (second, 3 behind Kessel) and a (-2), when Bonino was +9 and Kessel was +5... and he is awarded the Smythe. He had 11 points in 19 games and was (-3) against in the last three rounds, against teams that were actually any sort of competition. In total, Now it's all about how Crosby "won the Smythe in leading his team to the Cup." I can't even...
2017- Tied for second in scoring with Kane, 11 points behind McDavid. It's a strong season, especially considering he led in goals, but McDavid was in his second season at age 19/20 and hadn't even hit full stride, yet he beat Crosby's 89 points by 11. So in a couple of respects (Rocket, tied for 2nd in Ross) it's quite strong, and in a couple others (89 points, 11 points behind 19/20 y/o not yet at his peak), it doesn't seem quite as strong. The Pens win the Cup again, this time with an easier path through Ottawa in ECF & Nashville in SCF. Crosby's playoff performance was much better than in 2016, but his rankings were similar: tied for third in goals, second in points, and behind several other players in plus-minus. There's nothing wrong with his 27 points in 24 games (+4), and I wouldn't say he was particularly undeserving of this Smythe, but it was not a legendary performance by any means... about average for him on a per-game basis, as it would be similarly for many of his competitors for top 5... and the award could at least as easily have gone to Malkin (28 points, +9) or Kessel (23 points, +12), and may have gone to the goalie if not for injury (Fleury was very good, Murray was brilliant).
2018- 10th in scoring, behind teammates Malkin & Kessel, despite playing every game. He's also even in plus-minus (one of only three times so far he's been even or less) and had 29 goals (only other time < 30 in near-full season was 2015 with 28). He was strong in the playoffs, with 21 in 12, and with more goals and a better +/- than either of the previous two seasons in half as many rounds.
2019- He tied for 5th in scoring with Marchand, 28 points behind Kucherov. Similar to 2017, it's strong in some respects (100 points, although scoring jumped... tougher competition in Kucherov, McDavid, Kane, Draisatl, Marchand, MacKinnon, etc.), but still nowhere near competing for the Ross. He had 1 point and was (-4) while being swept by the Islanders.
2020- Injury cut into an already shortened season. Obviously unusual circumstances, but while 3 points in 4 games was okay, losing to Habs 3-1 was unexpected.
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SUMMARY:
I think what would be most unique about Crosby, if not for multiple seasons shortened by injury, is his amazing consistency. He was already an excellent player when he entered the NHL and he's still an excellent player today, 14 seasons later. Not too many players can say that they were an excellent player (when they played) for 15+ seasons. This would almost certainly be enough, on its own, for him to be in the discussion for #5 IMO, but one problem is that since his argument heavily relies on such consistency, the injuries derailing that consistency in value really hurt his cause.
Another thing that hurts his cause is that his peak wasn't better than that of his best contemporaries. While Ovechkin and Malkin are great in their own right, Ovechkin's peak was rather brief, and Malkin has lost substantially more time to injury than even Crosby has. Just using adjusted points for simplicity's sake:
Best Seasons
-----------------
Crosby-- 122, 117, 116, 106, 106*, 100, 99, 98, 96, 93, 91
Malkin-- 122, 117, 115, 100, 89, 87, 82, 80, 80
Ovechkin 122, 117, 114, 107*, 94, 92, 91, 90, 89, 88
Thornton 121, 115, 113, 104, 94, 92, 89, 88
Kane----- 119, 111, 105*, 99*, 98, 94, 79
McDavid 116, 113*, 110, 110
* = shortened season
If we take shortened seasons at face value in terms of adjusted points, average of top 4 seasons for each:
Crosby ~115.3
Malkin ~113.5
Ovechkin ~115
Thornton ~113.3
Kane ~108.5
McDavid ~112.3
Adjusted points aren't perfect, or even my most preferred metric for point production, and there are rounding errors unaccounted for here, but it still illustrates that Crosby didn't dominate his competition or contemporaries in peak point production. Kane lags a bit behind, but not that far, and the other five or very close... all within ~3 adjusted points of each other. That's with McDavid only having four full seasons to date (injured during his rookie year). Of course Crosby overtakes each and every one of these players due to his consistently excellent play, and that certainly suffices vs. his contemporary competition in this area, but the fact that 4 others that mainly overlapped his era are roughly equal (and a newcomer is quickly threatening to surpass him in this area) isn't a great start in perhaps the most universal starting point in comparing scoring forwards.
Another thing that is surprising about Crosby is how many playoff series where he laid an egg to some degree: '09 vs. DET, '10 vs. MTL, '12 vs. PHI (team meltdown), '13 vs. BOS, '14 vs. NYR, '19 vs. NYI, '20 vs. MTL (big upset)... and the last 3 rounds of the '16 Cup run, he wasn't particularly impressive (11 pts. in 19 games, -3). Players are going to have bad series from time to time, but he had a lot of bad series, some really bad series, and was particulary ineffective in most series against the stronger defensive teams. It's difficult to remember even single playoff games where Crosby took over a game against a strong defensive team. I think the same can be said of his play in the Olympics, despite playing on the best team, golden goal or not. The Pens were also fortunate to mostly avoid the real powerhouses, because they tended not to fare well: They lost to DET the first time, then had a lot go their way to win the second time in 7... were humiliated the one time they played BOS... and completely avoided CHI/LA. Considering how often it's argued that injuries really hurt his career, because he was so dominant when he did play... I don't really find the data to back that up. It's not that he wasn't a great player, it's just that his peak seasons and his playoff play against teams that weren't relatively weak/mediocre wasn't any better than the other greats of his generations, and certainly not head and shoulders above them.
I still think Crosby surpasses the best of his contemporaries, Ovechkin, but not based on peak brilliance and perhaps not even on playoff performance. To me, it's based mostly on his prime being more consistently great in terms of point production and in terms of ES value (basically, his plus-minus comparative data is better, probably because the combination of possession/defense is stronger for Crosby than Ovechkin). That's all well and good, but when he takes a step up in class (at least in some cases), and takes on the likes of Beliveau, Hull, Mikita, Lafleur, and Jagr... it's gonna be a really tough road, unless his career takes an unexpectedly positive turn in individual production.
