When I was playing NHL 2004 several years ago, I played a season of Swedish hockey and, momentarily, was confused when I saw what the standings were spitting out at me. I wasn't aware of a 3-2-1-0 system at the time, but once I became aware of it, it became my personal favorite.
I had a brief chat here about a week ago discussing some other alternative regarding a points system, one that doesn't reward losing in any way whatsoever, and I can go with that one as well, but the biggest benefit of a 3-2-1-0 points sytem is that every game has equal points value which, in turn, means that every season will see the same amount of points handed out as the one before it and the one that follows it. We've all been in that situation before with our team, scoreboard watching a game with two teams we're in contention with, and hoping that, whoever wins, that the game just doesn't go to overtime. We've also been annoyed many times when, predictably, that's exactly what happens. There's no reason for that. If the game goes to overtime, fine. Overtime (and shootouts), as it is in it's modern form, only vaguely looks like professional hockey anyway these days. You should be penalized for having to go to the extra session to win a hockey game.
It's just nonsense that some games are worth two points and some are worth three. And it's even more nonsensical that we've had this problem for, jeez, about 20 years now I think, and the problems with it were glaringly apparent on day one, and nothing has been done to fix it. I understand part of what makes the NHL the NHL is fixing the things that aren't broken (hello, offside challenges) while leaving the broken things undisturbed. Doesn't mean I have to enjoy that they're like that, though.