Great points, all around. But I'll just say that universities football and basketball (and soccer at UA) teams are the faces of the university. Those two (three) teams are generally the only reason a local population pays attention to a school.
I didn't attend UA (I had a tiny little athletics scholly to Malone) but I've been following UA since I was in high school b/c they wear "Akron" on their chests (I could never have competed at UA's level). Over the years I've given thousands of dollars to UA b/c of football & basketball. Sadly, I'll admit, not because of their world-class engineering programs. Again, not saying that's a good thing, but it is what it is. I know I can't be the only Akron-area resident who supports the U b/c it's Akron U.
One pet peeve of mine: when I'm wearing a UA t-shirt & someone asks, "Oh, did you go to Akron?" When I used to wear Ohio State gear no one ever asked me, "Oh, did you go to Ohio State?"
Oh, and let me add this, which I occasionally post: IMO there shouldn't even be an "Athletics" budget. Anything athletics related should be grouped under "Advertising/Marketing" b/c that's what D-1 athletics actually are.