I get all that but that why I said they could be more competitive and even win titles in basketball. When we talk about divisions we are typically talking about football and basketball for the most part but as you point out they don't participate in the FCS post season and only play 3 out of conference games (mostly against local or other non-scholarship team) so I'm not really talking about fb. Maybe I should have made it more clear but I think downgrading to DII would help their basketball and give them a chance to win some title which they DO compete in.
Same reason Dallas will never leave the NFC East. History. Would they be more competitive if they moved down? Sure. Do they care? Not really.
And also, they're good in the sports no one cares about (well, I guess to be fair, sports I don't care about). So they'd want to stay in D-I for that. And the Ivy League has had some pretty good teams in the tourney lately. There are plenty of schools in D-I that aren't competitive as the Ivy schools...and they have scholarships.
But something should be done with the D-I football situation. I do think it's ridiculous to have schools without scholarships competing against schools that do.