It's relatively common to see upsets in any of the first three rounds and exceedingly rare to see upsets in the Finals. The only one I can really think of is the Canadiens in 1993. Many point to the Devils in 1995, but forget that essentially the same team was an OT goal away from being the favorites in the Finals the year before. It was a shortened season, so there's no real telling where the Devils would have ended up in the standings in a normal year. As for Bruins/Canucks... that was a great Bruins team and just look at the record of the other teams in the Canucks division. It was like the old Southeast, but worse.
If your goal is to just get there and be competitive, anything can definitely happen. If you want to win it all, it requires having the same or more talent than the team from the other conference.
Eh. First of all, I doubt the Devils would not be underdogs against the Wings team even in a full season. Second, I think you're putting too much stock in an at most 7 game sample size. Too much luck involved to say that the likes of the Flames and Oilers lost by their one goal because they were less talented. And it's not a large leap from competitive to winning a series in the NHL in a 7 game series. So much luck involved and goaltending plays a huge role that if a team is competitive then likely with some luck they could have won the series. Even in series where I don't think a team would beat another team in a million years in a best of 7, you see wacky results. The Hurricanes were mediocrity personified faced perhaps the best team since the 80s Oilers (very arguable but they were great), won a game and played an OT and a 1 goal game in the cup clinching game. They didn't even allow more than 3 goals in any of the games. That has to be one of the biggest talent discrepancies in SC Finals history and it was ridiculously competitive. There are zero teams in the NHL IMO that are as much better than us than those Wings were over those Canes. The Canes weren't winning that series, but it's amazing how competitive that series was and the talent was almost comical.