You said that often teams that are comfortably making the playoffs take their foot off the gas in order to save themselves for the playoffs. But Presidents' Trophy teams by definition are comfortably making the playoffs, so wouldn't they also take their foot off the gas?
Maybe not if they haven't won a Cup already. I said I know for certain the Hawks would take their feet off the gas. I'm positive the Lightning did as well. Maybe the Rangers, Panthers, Bruins, etc...had something to prove to themselves having not won the Cup yet? So they went balls to the wall all season trying to maintain their excellent play in hopes it carries into the playoffs.
-Bruins won the PT in 2013/14 after losing the Cup Final the year before
-Rangers won the PT in 2014/15 after losing the Cup Final the year before
-Nashville won the PT in 2017/18 after losing the Cup Final the year before
-Tampa smoked the whole league in 2018/19 with a whopping SIX more ROW than 2nd place and all it got them was a first round exit. The next year they finished 4th and won the Cup, the year after they finished 8th and won the Cup. Both years with incredible rosters.
-The Bruins won in 2019/20 after blowing a SCF game 7
-Avs came out in 2020/21 with everything to prove as the new elite team on the block, won the PT, lost to Vegas (handedly) in the 2nd round, came back and won the Cup the following year with a better roster but finished 2nd
Whereas the more seasoned and successful teams know the regular season means little beyond making the playoffs, not even the seeding/home-ice matters that much. It's not that they don't care about winning, just that it's not worth it trying to be the best regular season team when you have to save your legs for the postseason.