completely disagree with your first sentiment in 2011-2012 Chicago finished 6th in the west and lost in the first round partly because players like Kane were poor, then with basically minimal chances last year they came out and were the most dominate team in the NHL because players like Kane took his game to a different level. Kane had 66 points in 11-12 in 82 games where as he had 55 in 47 last year(95.9 point pace over 82 games) how that's not stepping your game up to a new level I don't know. he wasn't the only one to do it and that's why they won the cup.
I see it in a very different way to you. It happens all the time that a team has a weak year, and all the players on a team put up weak numbers, then a team has a strong year, and everyone puts up strong numbers. Even last year alone Chicago were hardly the only example, Anaheim did the exact same thing (went from weak to strong as a team, and tonnes of players had their individual numbers improved substantially).
People like to have really simple cause-and-effect explanations for every little variation, like "this star improved tremendously and carried the team with him," or "this star had a bad year, so his whole team sucked." In reality there are an infinite number of factors influencing how a player AND how a team can perform. A team playing well can mean more time in the offensive zone, and more points for most players; a coach adopting a more offensive or more defensive strategy can affect everyone's point totals, AND the team's success; luck plays a HUGE role in sports, much more so than most will admit; etc.
People love to see "X happened because of Y" type logic explanations everywhere in the world, when really the explanations are way more complex. When I look at the variance in Kane's PPG over time:
I really don't see last year as him getting way better as a player, or the year before that as him getting way worse. The most likely explanation is that he's more or less the same player, with the same talent/abilities/drive, but other factors are causing noise in his production. Watching Kane play he's looked like more or less the same player to me for the past 4ish season straight, with people just reading way too much into pretty standard variance.
I work as a Data Analyst for a fairly large tech company, and I see this all the time at my job. When we're at point A in the chart below, everyone is freaking out, and wants "THE reason why this metric is so bad this month/week/whatever!?!?!?!?!?!?!" When we're at point B, it's always "look how amazing this metric is this month/week/whatever, it must be because of my business initiative!!!!!!"
In reality there's no single reason why the metric went up at A and down at B, it's a result of a huge number of factors, many of them virtually impossible to determine, and many of them complete outside the business control, and more whims of the consumers. When you're in the middle of that good period or that bad period, what is basically just noise can seem like some hugely significant trend, but it rarely is.
It's the same in sports, and pretty much everywhere in life. Human beings always want simple explanations for things that just don't have simple explanations, and we love to see trends where there really aren't any.