management business.
One problem with your scenario is the aspect of competition. Costs will continue to spiral even higher. Donations will entirely dry up (why donate if the for-profit arm is managing it? It is their job to make it successful, not mine). If the majority of top athletics programs run in the red already today, how is a school like BYU supposed to run a profit given the constraints we are under (no Sunday play, limits recruiting pool in both athletes and coaches, etc)?
You'll see athletics dropped entirely well before you'll see the Church take it over.