I think this is waaayyyy too simplistic. Let me argue your simplistic view with my own...
If not for BMDs and Regents, UT Football would have very little support. It's been stated elsewhere, but by and large the faculty loathe the football program due to all the money it spends. The student body is becoming more disassociated with sports in general.. The Administration really doesn't care about the program's competitiveness because successful or not it generates a ton of revenue. All they really care about deep down is that the money rolls in and the program doesn't create legal or political problems for them. So yeah, I think billionaire alumni with egos that want their team to beat other billionaires' teams is fundamentally what's driving (and funding) our ability to compete. Without those egos and the money behind it, I'm not even sure where we'd be... probably a Berkeley... Which is what we'll be in 15 years anyway (I truly believe, as these old BMDs die off and new moneyed alumni just don't care as much).