I'll also add that University of Chicago dissolved their football team because they saw it as corruptive and counterproductive to the mission of education...in 1939!! (They brought it back 30 years later, but as a small-time Division III team with no scholarships, not the national powerhouse it once was.)
The Ivy League of course does not offer athletic scholarships, although some are facing criticism of surreptitiously lowering admission standards for big sport athletes.
And Vanderbilt University did something interesting recently:
In September 2003, Vanderbilt earned national attention when it announced that it was eliminating its athletic department. Then-Chancellor Gee called Vanderbilt's varsity athletes "isolated", and insisted that student-athletes would perform better if they were integrated into the rest of the student body. So rather than administer athletics separately from student life, Gee folded the university's varsity teams into the Office of Student Life, the same group that oversees all student organizations. The university is unique in Division I in this regard. Despite fears that Vanderbilt would lose coaches and recruits or would be forced out of the SEC, the university has experienced considerable success since the change; 2006–07 was one of the best in the school's athletic history. At one point, seven of Vanderbilt's 16 teams were concurrently ranked in the Top 25 of their respective sports.