That's the case in the past and certainly the case presently. But I'm not certain it has to be the case in the future. When I was growing up most of the better students in the state wanted to attend private universities if they could afford it. That isn't the case currently. Things change.
It remains to be seen if the university can capitalize on this and get students excited with its sports. I think they can because some of the reason these students are choosing UConn is because of their successes in sports.
The university has to undo some of the damage that occurred with its passionate fan base. Some of it was lost over the past few decades with the seating policy changes. But I'm convinced, as I've stated in other threads, Ct has passionate people who love sports and are no different than other places. UConn certainly is in competition with other venues and that makes it harder to promote itself than a Kentucky, but that doesn't mean it can't ultimately be as successful as Kentucky.