You realize that they can still play defense, right?
This would be the perfect set-up for the majority of KF teams that had a strong D and special teams but questionable O. Kickoff, play D, get the ball back with a short field, game over.
The flaw in the college system is that you're basically automatically guaranteed a FG and leads to too many multiple-OT games where neither defense can get off the field. As noted above, the results of a college OT game are generally far more random and much closer to a hockey or soccer shootout than in actually reflecting who is the better team and more worthy of winning the game.
The perfect way to do it, which will never happen for a multitude of reasons, would be to play an entire quarter or half and see who's ahead at the end of extra time, like association football (soccer).