The reason they don't do the 3 pts system is simple:
It is the best and most fair system. It is illogical to make a team get 2 pts for a overtime/shootout win while another gets 1 for losing creating both 3 pt and 2 pt games. It is also unfair that a team that wins in regulation gets the same amount of pts as one winning in overtime/shootout.
But here lies the problem: The standings would be too imbalanced by mid-year. The better teams would make the playoffs, and the worse teams would be so far out that nobody would even pay attention and they would start thinking about next year. The NHL doesn't do the system because it would cost them $$$
Maybe - but it depends how you look at it.
I'm a habs fan. As of this posting, we're 8 points out of a playoff spot, with 1-2 games
more played then the last WC/divisional spot. 32 games to go - so almost half the season. Under today's system - we are not exactly mathematically eliminated or anything, but we're so far behind, the odds of us catching up and qualifying are extremely low. We basically need to win 8-10 games in a row, while those last place playoff teams go ~500 in the same stretch - just to catch up (not even pass them). Then we still need to outperform them down the stretch to finish ahead. So - very long odds.
Under the 3-2-1 system? I find the odds a lot more attractive. We're far back? Lots of ground to cover? Great - time to take more risks in regulation. Instead of just 2 points - we can now get 3 points in a regulation win.
If this were the last 2 weeks of the season - it would make for some explosive standing battles, both for last playoff spot but also for top of divisions. I remember how close the east was contested at the end of last season for last playoff spots. Montreal, Columbus, Carolina, Pittsburgh, Toronto...just imagine if teams had the ability to go for 3 points in a game. Would allow for a lot of wiggle room in the standings, and make things even more unpredictable.