NFL Overtime Rule - Simple Fix

I feel like a lot of people have a problem with the randomness of the coin flip determining possession.

Would the it better if possession was earned by something done on the field? I propose that the team that leads in time of possession be awarded the ball. Control the ball during the game to earn the right to control the ball in OT.

Using time of possession to award the opening possession seems to penalize teams that pass rather than run. Why should that be the determining factor?