I don't know, getting rid of the loser point might push more games to OT and SO as opposed to having the opposite impact. With the loser point, teams at least push harder for the win, knowing they have the safety net of the single point. If you take that away, they might be more cautious and take there chances with the SO.
The problem is that there's so little incentive to win in regulation and the overtime is too short. If the game is tied in the 3rd period, they will make sure they get their point before they try to win the game. That's where the problem of the short OT comes in, because try as they may to win, it's hard to score with only five minutes to do so. The end result is a lot of shootouts.
Here's the best way to cut down on shootouts, IMO:
Use a winning percentage based system, or 2 points for a win and zero points for any kind of loss, if you want to keep a points system.
First tiebreaker in the standings is regulation wins.
Second tiebreaker is regulation + overtime wins.
Overtime format of 10-minute 4-on-4, with goaltenders switching ends after the 3rd period. Then a shootout.
The problem is that the extra point for reaching overtime is too enticing for teams to risk by opening the game up in the 3rd period. The second problem is that a 5-minute overtime is generally too short. Hence, you end up with a lot of shootouts.
So you remove the incentive to reach overtime and you extend the overtime period to give teams more of an opportunity to end the game without having to play a shootout.
The other alternative is two points for a regulation or OT win, one point for a shootout win, zero points for a loss of any kind. I can't support any system that rewards losing.
Either way, it downplays the impact of the shootout on the standings and encourages teams to win in regulation.
As long as there is a reward for reaching overtime, teams are going to be all too willing to let a game get to overtime.