Post-high school football and basketball should be separated from education and run like the farm systems for baseball and hockey (US). Opponents of this idea tend to drag out a "but what about the korfball team?" argument, but I don't think it'd change those sports at that level too much. With any justice the big sports would have been contributing to an endowment for the smaller sports all these years that would be used for a future without stadium sports at the university level.
A big-market sports program is not necessary. Many accredited universities offer sports management and sports marketing degrees, both undergrad and graduate, and most of the ones I just googled are at schools known more for their academics than sports programs.
If I read between the lines correctly, I'm skeptical that students majoring in sports backoffice do any work at all in the school's own sports programs. Like maybe some interships? Access to some people for research and writing? I'm thinking: not enough to justify keeping them linked, and even so, the teams/sports would still be in the area. My point is that as far as the school is concerned, the potential for any overlap at all is slight. This is proven by the success of backoffice programs at schools with uncompetitive teams.