The regular season was a success primarily because of the talent level on this team. The Celtics have some bad habits that stretch back multiple years, but that didn't show up as much or in as pronounced a fashion during the regular season, because they weren't playing good teams every game, and their talent was often able to simply outgun the competition on offense. But now, in the playoffs, they're facing a really good team every game, the Cs can't just mask their mistakes and bad habits, and the heat (pun not intended) of the playoff crucible is sending all the crap bubbling to the surface.
Because of all of this, I think it's basically a bad idea to have a young, inexperienced head coach, because now he's gotta catch up to the experience level of the players, which could take several years, and that might be too long.