At many schools, the football and/or basketball programs literally fund all other athletics programs...including the scholarships for those other athletes.
Some schools, like LSU, have reported a 100x return or greater on their investment in their football coaches salaries, with respect to increased alumni donations, memorabilia sales, etc.
LSU alum here, and I can confirm that our athletic performance is a rising tide. It's my understanding though that LSU athletics pays employees from its own revenue. So it's not like LSU is diverting funds meant for academics to athletics (in the macro sense). As an alum I frequently get asked to donate to the LSU Foundation which is an entity separate from the Tiger Athletic Foundation, which is where you can donate specifically to the athletic department.
Some schools, like LSU, have reported a 100x return or greater on their investment in their football coaches salaries, with respect to increased alumni donations, memorabilia sales, etc.