Even if that were true on a game to game basis, there's no way it's more random than something like the NFL where it takes three wins to get to a superbowl. All that randomness is somewhat mitigated by having best of seven series. I think it's why you'll see unlikely teams make it to the cup finals every few years, but rarely ever win. Either the luck can't sustain itself for that long, or the other team that made it is so good that the lucky team can't outluck their way to wins. That's usually the case, because they made it to the cup finals.
Sure, luck is a factor, but you can't really control for luck. You can try to control how good your team is, and so the best thing to do will be to construct the most sustainably good team for as long as is feasible and hope that quality and luck end up on your side every few playoff runs. I think that was the point. There are so many cinderella teams that have been curb stomped in the finals, that I really can't understand how people can have such a positive outlook on mediocre teams making championship runs. I'm not saying that's what you were implying, but I still think it's one of the weirdest cliches in hockey. The playoffs generally aren't that unpredictable in a high level sense. Pittsburgh, Chicago, and LA won nearly every cup from 2009-2017. That Boston team is the only exception. From 95-2003 it was Detroit, New Jersey, Colorado (and of course Dallas with it's 99 win!). In the 80's it was the Islanders, then the Oilers, etc. etc. Good teams tend to win out, apparently in large chunks for nearly a decade at a time.
Arguably, this cap era of hockey should be more random because teams can't outspend smaller markets as much to really dominate, but good teams seem to find a way regardless.