I don't really like how college resolves ties. It doesn't feel like it properly represents which team deserves it. Like penalty kicks in soccer.
I believe there is a really simple way to fix NFL games from having ties and it fixes another problem as well:
The victory goes to the team that took the most recent lead change.
In this case, Green Bay would not have just kicked a field goal. Dallas had the most recent lead change, so they'd have to go for a TD if they wanted to win.
The other problem this fixes? The coin toss for OT. We went from the obvious choice was take the ball to the obvious choice is to kick (because you are guaranteed at least 1 possession and you'll know what to do). Moving to most recent lead change you may want to try to take the lead first in OT OR you might want to see what you have to do. There's an interesting choice there.
If nobody scores in OT, the victory goes to the team that had the lead before the other team tied it to go into OT. They had the higher percentage of winning the game before it was tied. Makes sense.
I will admit a possible flaw in this concept is a team might try to just run out the clock in OT knowing they had the most recent lead in regulation.