I'm sure you don't. Regardless, I suspect that this may be less causation and more correlation. Said differently, a lack of commitment to success often shows itself in more than one area. Just as a commitment to success does. Rutgers and UConn are good examples of this principal.
Rutgers is committed. That's why they just joined the B1G. They committed hundreds of millions to athletic facilities to prove that commitment. Meanwhile they were cutting academic programs willy nilly and dropping 20 places in the rankings. There are a lot of schools that built out. Many of them are losing, and dropping.
Others, that showed little commitment to athletics, and indeed so little that they dropped football, are rising. Most of the schools ranked in the top 50 universities in the USA do NOT have P5 or D1 football. Do they have a lack of commitment to athletic success? Yes. 32 out of the top 50 on US News.
In isolated cases, you'll find correlation between athletics and academic success. For most schools, that's an illusion, a dog and pony show.
Remember this: university presidents get paid a lot of money. For as long as they can hold onto their jobs, they will make millions. If they rock the boat, they can be fired. What's the incentive for them to make astute business-like decisions about cutting their losses? There is no incentive. This is why only strong leaders like John Silber at Boston U. (or leaders who realize the greater community probably won't care, as at Hofstra or maybe Temple in the future) can slash athletics when the school is losing big dough. Other people who makes similar decisions, like Elsa Benitez at Texas A&M (who asked the AD to pick up its surprise $18m shortfall one year) get the axe. She should have kept her mouth shut and continued to collect her half a million. When you pay people this much money, they have every incentive to do what they can to continue in their position as long as possible. This is more or less how the USA runs today.