The support for ties is not based on that idea. I remember pre-OT hockey so this isn't hypothetical. The support for ties is based on the idea that they happen in low-scoring sports and trying to "fix" them leads to crap like 3 on 3 keep-away.
Shootouts suck, but at least they mimic something that can happen in-game. Soccer is far and away the most popular sport on the planet Earth and soccer games end in ties regularly, so the argument that it's unbearable is flat nonsense.
BUT, if the league insists on a winner for every game then skip the OT nonsense and go straight to penalties, and reward those winners with full value. The NHL shouldn't be able to have it both ways: I.e. we want winners, but somehow they're not real winners. But since shootouts are a weak way to end a hockey game, I'd be ok with a regulation win = 3 points, SO win = 2, and a SO loser = 1.
The system they have now 100% rewards teams for playing to get past regulation and provides a tiny incentive to play hard for a 60-minute win. It's weak sauce. Period.