Well... University of Alabama, who (apparently) has a mildly successful football team is the fastest growing state flagship university in the country. 

They saw a 58% increase in enrollment between 2006 and 2016. The students choosing to attend also got better: Their average GPA was 3.66 vs. 3.4. The top quarter scored a 31 or better on the ACT, up from 27. Only 43% of students are from in state. 

Also, the football team was pretty good during that decade. 

No, most athletic programs are not self-supporting, but Oregon's is. And, like Alabama, Oregon's athletes draw students to the school.

NY Times story on Alabama: https://www.nytimes.com/2016/11/06/education/edlife/survival-strategies-for-public-universities.html?_r=0