Ivy Leagues are automatic, but if you are not working in the world of academia, the public doesn't know about the schools programs. Advertising is the only way to get the message out. Having strong sports programs is a part of advertising. If you think about it, the school (conference) gets paid when playing on a big network. Yes, that is income can be used to strengthen the schools programs.
While all this is going on, future prospects become attracted to the school & student population grows.
"Well that's a good but unproven theory there Mr. Chanson."
BS- Ask Texas, TX A&M, UCLA, Florida, FL St, USC, Ohio St, Michigan, etc.
The board of regents would totally be cool with it, because not only is it more income, but it will never reach the main schools status, because they have been ahead of the curve for a long time.
Sorry for going off, but it takes money to make money. Just follow the blue print set by other schools & don't try to re-invent the wheel.