You are oversimplifying the educational system to a very large degree (pun intended).
Education isn't about the 'information', it's about the collective sum of benefits that a university provides. If it were strictly about the education (courses, books, etc.) there would be no purpose -- most of it can be found for free online.
University is about the whole package, of which a strong alumni network is often a major piece. Without a strong sports program, many of these schools would lose a large fraction of their alumni's attention - and I don't mean dollars and cents. To use a previous commenter:
Ding ding ding. I went to a D3 school for football, and when considering a possible MBA, something I was looking at half jokingly, but half legitimately, was whether the school was large - because I thought it would make watching sports on TV for the rest of my life, and having true attachment, a lot more fun.
Undoubtedly, as I progress further in my career, that fervor would have grown with team success, and also made my attachment more real - while my current alma mater (Chapman University in Southern California) - would have fallen away from consciousness with no legitimate way to grab my attention.
Whether I make a donation to any school in the future is up for debate, and I am now not likely to get an MBA based on many of the points raised here and elsewhere - but the point made on this comment hits the nail on the head.
I find it extremely unlikely that I will ever donate to my small private school in Southern California - because the thoughts of how it's helped me depart with every passing second, and they have no way to get it back.
This obviously leads to a weakening of the school on a whole, in terms of future enrollment and overall reputation, leading to a decline in the quality of education.