The "Cup or bust" mentality has always been pretty toxic. It does not suit very well for the league of 32 teams where it's only one true trophy to win. Add to this salary cap parity, draft/trade system, and the fact that if your current core has aged and past its prime, you may need to wait a lot of years before your team will again be just good enough to have a realistic chance for a playoffs.
It leads to very good teams being underaprecciated for a long time because they didn't win the Cup...right until they do. From last 6 Cup winners, 4 of them have won the Presidents trophy in a year or two before they won the Cup. And then the narrative changes completely, with the appearance of revisionist history.
Add to this random and chaotic nature of the sport itself and injuries. There is a significant chance that management can do everything as good as it can realistically be possible, build the proper core, find right coach and depth players, ensure winning culture among the organization...and still not win the Cup because of whatever, f.e., random bounce in OT, your best player injure himself by falling awkwardly, opponent's goalie suddenly playing best hockey of his entire career, etc. That unpredictability and randomness makes the sport fun in such a unique way, but doesn't make a lot of hockey conversations fun. "Cup or bust" mentality doesn't really make the Cup win sweeter, but it makes losing much more bitter and increase the overall stress.
Any time i see hockey discussions, there are too many "chokers" and "losers" for me to handle.
In European soccer, there are more than one trophy each team can win every year, such as national cups, and although they often considered as lesser ones, they're still legit. The system works the way that if your club is strong and has a good chance for winning trophies, it is likely to remain for a long-long time. And even if your club is not that rich and succesful, it still could win national cups for example (because it doesn't require to play with a lot of teams or with any team for a lot), which would be a pinnacle of its existence.