The thing about private schools having the money is that just about all of them lack the culture required to host an FBS program. Administrators/faculty tend to be very anti-sports at several of these institutions.

It's political willpower, not money, that holds back most semi-rich to rich private schools. I'm sure that most of them could play in FBS if they really wanted to - but they don't.

Another thing to realize is that most of the campuses are not in ideal locations (if you're talking about urban privates). It costs a fortune to acquire land rights alone - and that expense doesn't add up if you lack rivals and/or a landing spot to go to.