The other player I wanted to talk about (to preemptively address why he isn't on our final list) is Scott Niedermayer. I could have sworn there was a recent list on the NHL's website which showed him as a top ten defenseman all-time. I can't seem to find that, but I know he has some vocal supporters.
Through the end of the 2003 regular season, Niedermayer had a fairly unimpressive start to his career (by the standards of a top 100 player - consistently playing 24 minutes a night on the NHL's second best team during that period is objectively very good, of course). Through his first 11 seasons, I'm not sure that I'd rank Niedermayer higher than Sergei Zubov (a borderline Hall of Famer who isn't up for voting).
We all know that Niedermayer was a first-team all-star and Norris winner or runner-up each of the next three years (2004, 2006 an 2007) - but he started his peak during the 2003 playoffs, when he was the best Devil en route to their Stanley Cup victory. Because Niedermayer's peak was so late in his career, a lot of people seem to have "projected backwards" and assumed that he had played at that level his entire career - when that simply isn't true. We all know that the Norris trophy voting is imperfect - but I find it telling that he didn't receive a single vote in eight of his first eleven full seasons.
Some people have argued that Niedermayer's stats were suppressed by playing in New Jersey (as evidence by him scored 60+ points for the only time in his career once he left the Devils). I don't think that's the case; his scoring spiked after leaving because offense around the league jumped those two years. Based on hockey-reference's adjusted stats, there's only a 2 point difference between his two highest-scoring seasons as a Devil, vs his two highest-scoring seasons as a Duck.
Leetch was just voted in last round, and there should be a gap between them. Both played 1,200+ games; both had one decade to their career that was clearly better than the other. The difference in their offensive production, even when making reasonable era adjustments, is not small (in Leetch's favour). Niedermayer is better defensively but not enough to clear the huge gap offensively. Both had a Conn Smythe but Leetch's was dominant; Niedermayer's was undeserved. Leetch was top five in Norris voting seven times in a tougher era compared to four for Niedermayer.
Many people use Stanley Cups as a trump card. There's no denying that Niedermayer was an important contributor to many championship teams, but as I showed in the post about playoff R-On/Off, his team almost always fared worse when he was on the ice. Context matters, but I don't think it helps his case that, for almost his entire playoff career, he had an even better defenseman taking the toughest match-ups (Stevens in NJ, Pronger in Anaheim).
One interesting thing about Niedermayer is he wasn't a huge contributor to special teams. From 1998 (the first year we have ice time data) to 2007 (the end of his prime), he was 3rd among defensemen in ES ice time. But he was only 11th in PP TOI and 34th in PK TOI. This was unusual compared to top defensemen of his era. The same was true of Mark Howe, but at least in his case he had dominant ES results - Niedermayer doesn't.
Despite all this, I think highly of Niedermayer. He was just outside of my top 100. Maybe he deserves a spot if you're counting Cups and place a very high value on peak play. But there are too many players who have been all-star level players for much longer periods of time.