I might be way off on this, but Monty reminds me a lot of Bruce Boudreau both in terms of having tons of regular season success with very little playoff success to go along with it and just overall approach to coaching. Both seem like easy-going, likeable guys who emphasize good vibes and fun at the ice rink which keeps players happy, motivated and successful during the long slog that is the regular season. When rough waters hit or when the intensity jumps up during the playoffs, however, it seems like they both struggle to maintain success because so much of their coaching approach is dependent on their team feeling good rather maintaining discipline or making strategic or systemic adjustments which results in them and their team getting flustered and unraveling.
Regarding Monty's past two playoff appearances, I agree that the results are about what you would expect given the rosters but would argue that the way he ended up with those results leaves a lot to be desired. Last year against the Leafs, up 3-1, that series should not have gone seven. Period. Who knows, if they had taken care of business in five or six and were feeling confident rather than letting those playoff doubts linger and fester, maybe they put up a better fight against Florida in the second round. This year with the Blues, blowing a multi-goal lead in the last minutes of the Game 7 to lose is starting to feel very on brand for him, regardless of the circumstances. While Monty definitely deserves credit for taking a mediocre Blues team and pushing the league-leading Jets to the brink, I'd argue that how much of that was him and his coaching is up for the debate as Winnipeg was battling through some pretty major playoff demons (and injuries) of their own.
As you said, it will be interesting to see whether he learns with experience. For my part, I certainly hope he doesn't (at least not anytime soon). I'm already sick enough of hearing about Cassidy all the time haha.