You are correct on the media market. Look at the Alabamas, Clemsons and Notre Dames of the world. One thing they all have in common is that they're the biggest sports in the local media. I think it's hard to find a college team at a really high level when they're in the same market as an NFL or NBA team. Kids wanna be the top dog in the sports section not page 2 after the local NFL team.
Case in point would be Gopher football,considered a national powerhouse until the 60s when who moved to town??