Hell what if Mark Cuban offered $3 billion a year for the 40 best football programs to play in a league he creates. They leave their other teams in the conferences as they are now. You don't think the big boys would jump at that.
No...they won't. Reduction will not happen, especially into the private realm like in your example. Too much risk to lose their tax deductions, tax favored borrowing, and general tax arbitrage (already identified by the CBO and by default, at risk), for both the athletic department and the university. That is a bigger deal than what cash would result from a private league.