The way I see it, if SU chooses to have a football team, they need fans. To get fans, they need some kind of tailgating culture. And to support tailgating, they need on-site surface parking (which I really don't like in most contexts as well, for the record).
On the other hand, like 20,000 SU students get by in their walkable urban environment every day without a car, evidence that car ownership -- to say nothing of car availability right near the core of main campus -- is not a necessary part of student life at SU.
So while I agree that students should take priority over visitors in most cases, I don't think their contribution to the institution is as dependent on 8-hour blocks of car storage as the tailgaters' is.