Just re-doing the standings with a 3 point system assumes that the games are played the same way under a system that functions properly. Current coaching strategies reflect success, which in turn reflects the fact that a goal prevented is worth about three times as much as a goal scored, solely because of the loser point. It might take a while for the league to adjust, but a 50% increase in points in the standings is not a small thing, and teams that "go for it" and succeed would be the class of the league. The class of the league tends to be emulated, because this is a copycat sport. It would make a bigger difference as the season goes along, too - teams chasing playoff spots being more inclined to play aggressively.
Just mathematically, by the way, this is wrong:
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I don't necessarily agree that making a regulation win worth 3 points is going to make conservative coaches risk guaranteed points available in extra time just to get that extra point. I feel plenty would be happy playing conservative to ensure one point over going for it and risking zero points.
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Assuming everything else is equal, if you go to overtime in a 3 point system, you're either getting 2 points or 1. Your point value is 1.5. If you go for broke in regulation, and we assume the game ends before OT, you're getting 3 points or 0. Your point value again is 1.5. Of course, things aren't equal, and teams that press tend to have more success, which is why trailing teams tend to produce most of the offense in a game they're behind in.