Making assumptions is hazardous. I grew up playing sports, and I watch spectator sports. I've also attended universities which had athletics programs and universities that only organized (but did not pay or charge for) participatory extracurricular activities, like intramural sports (and the clubs you're worried about). The difference in academics, social cohesion, and corruption were very noticeable, and none of those differences favored the schools with athletics programs. I think you'll have a difficult time demonstrating that these athletic programs actually help the school financially. They usually cost the school a great deal, and their expense is generally justified by claiming the programs are good PR (but considering the number of scandals associated with athletic programs, I think this is a silly argument).I'm assuming you're not a sports fan. I'm a huge sports guy.
Athletics are huge money draws for schools