There is definitely a pendulum effect (BESIDES the salary cap) to winning NHL teams. We saw it with our local boys the Kings. I won’t say winning the Cup could ever be done on psychology alone, but it helps. You know a strong will, a tiny very into it town, really can get you to a series win from being down 0-3. Skill is hella not enough!
When the Kings are doing well, the entire town (Manhattan Beach, where they ALL live) is abuzz and displaying signs, stickers, gear. The town is that seventh player in MB for sure.
And then, when you are at the top for a few years, since there is no where to go but down, other teams have MORE motivation than you do to win the cup, and your salary cap for the hottest players means they need to sacrifice in order to stay, so the order of teams always changes at the top. Which is, in the end, fair and makes the playoffs so exciting.
L.A. is a tough town for any team to succeed. The biggest problem there seems to be the enormous size of the metro area coupled with the wide variety of entertainment options there. They went years without an NFL team, and NASCAR even took away one of the race dates at California Speedway because of the low attendance.