I'm with Slayer/Kotz. You had 60 minutes to win the game in regulation. If you can't do it then, then not getting your offense on the field in OT is 1 of the risks you run.
College football is about the spirit of competition (LOL - I know, I know), so the matching possessions make sense.
For the matching possession proponents, what would be your plan? Exactly like college? Or only do matching if there's a score by the offense on their 1st possession?