EDIT: It would be very hard to shift funding from sports to academics because it's a cultural thing now. People are much more readily accepting of spending x million dollars to build a new stadium than to build a new research facility.
Citation or definitions needed.
For example, while Stanford is elite in some ways, it isn't a sports school. However, its "big athletic programs" (football, basketball, baseball, and possibly tennis) are more than self-supporting via directed donations and tickets.
The profits are used to fund less lucrative sports.
Yes, including the newish football stadium.
Your perception is almost entirely wrong.
And yes, that includes the new football stadium and the newish tennis stadium.
http://www.outsidethebeltway.com/archives/college_sports_a_m...
Do you have sources for the belief that sports pay for themselves?
Really? It appears to me anecdotally that the run-up in tuition has been accompanied by a run-up in university building programs. My alma mater, a large state-related research school with a big sports program, is nearly unrecognizable ten years after I graduated, with a new IS building, a new science building, a new business school building, and a new law school building.
The university did charge an athletic fee. This was to cover the publicly accessible tennis courts, basketball courts, football, baseball, and soccer fields. They also provide buses for the intramural teams. And part of it went to subsidize student football tickets to the nationally ranked football team, played in a stadium the football boosters paid for.
I've watched the college next door to me transform from a small community college to a full fledged university. And they got there by having a serious athletic program.
Sadly, you're probably right about this. Sports seem to have become so ingrained in the popular paradigm of what you do at a university that it would be impossible to change. Oh well.