It must be a difficult dilemma for major college presidents. On the one hand they have this massive revenue stream that they have a fiduciary duty to protect and enhance. OTOH their mission, and their background, is education and it has to be uncomfortable for them to see so many demands made by school supporters on behalf of the football/basketball programs. At some point, some of these people may say that it's just not worth the hassle; we're gonna be the best university we can be without football being a big deal here.
I think you overestimate their mission and background
How so and at what types of schools? I think the presidents of Northwestern, Duke, Vanderbilt and Stanford (their recent success notwithstanding) will have a very different take on football's role at the university than will the president of Alabama and Texas.
Though it's also interesting to note that the four schools I mentioned are probably loaded with wealthy alumni who could easily endow 100 football scholarships and stipends. Now finding 100 recruits who can meet those schools' academic standards may be an issue but it's still fun to speculate what might happen.
I had an amusing discussion with someone at another board who was concerned that the elimination of amateur players in college football would mean that Northwestern or even
Yale could win the national championship by virtue of their rich alumni, as if that signaled the beginning of the apocalypse. Are only the Alabamas and Oklahomas allowed to win football titles?