So here' s my proposal:

When a game ends in a tie you play some amount of 4 on 4 (5 minutes, whatever - sudden death, golden goal if you like), and if nobody scores, then both teams get zero points.

Why is this a good idea?

1) It'll make the end of games far more exciting. The original reason for pity points is that teams tied late in a game were playing conservatively not to lose, and this was really boring. With this system there is nothing to protect and everything to gain at the end of the game. In fact, if the OT is sudden death (someone scores a goal and it's over), then that means the players can't even let up for a second. That's going to make some intense, high stakes hockey right there. So it'll be entertaining.

2) it’s satisfying on a meta level – if you don’t win anything, you don’t get anything -  every point is an earned point. When you pick up points on essentially a coin flip (and a loaded coin at that, in the case of the Leafs), their value as markers of achievement is devalued. When you have to fight and claw for every single point, then they become MORE meaningful instead of less. And that's how sports should be.

3) It might mean more eyeballs for the NHL. Not only do the end of tie games get way more exciting (which builds value in the basic product), but fans might even  watch 2 teams they hate play (or at least the end of a tied game between them), which they would never normally do – because now they really CAN cheer for everybody to lose. That’s a win for the NHL because more eyeballs watching more teevees translates to more dollars from tv networks. And, all evidence to the contrary, the NHL really does like dollars.

4) The record books could become far more interesting. If you only reward actual wins, and stop dishing out free points when they just barely squeak by, then the true epic futility of the absolute worst teams can be posted in all its glory. And horribly unsuccessful franchises (clippers anyone) are part of the lore of sports. It makes the NHL a richer and more storied place to have a few teams like that now and again. Plus, in the short run you might get a few entertaining storylines towards the end of the season about the absolute bottom feeders - can they escape going down as the worst team ever (with a few asterisks for the different accounting system). That could keep a few pundits and fans busy,which I'm sure they would thank you for in a small way. Economically speaking, sports is a form of entertainment, which is why adding entertainment value is how you build actual dollar value. 

That's a pretty solid case is it not (particularly the first 3 points)?