Here's the main rule to surviving as an independent in today's world: is your fan/alumni base tied to something *other* than geography/market/home state?
Notre Dame = Irish Catholics
BYU = Mormons
Navy and Army = Military
They can survive as independents in today's world because being in a regional conference really doesn't do anything for their respective alumni and fan bases. These are legitimately national fan bases. Even then, it can still be tough being an independent, as shown by Navy still apparently committing to coming to the Big East.
Schools like Idaho and New Mexico State aren't independents by choice and they don't have the national fan bases can't deal with that environment.
UConn simply doesn't fit the profile of a school where it makes sense to be an independent. (To be sure, even schools such as Texas and Ohio State don't have the profiles to be independent, either.) I'm not saying it's an easy call since I've been saying from the get go that the Catholic 7 was going to end up getting a much larger TV deal than expected in the now-football-centric conference realignment analysis and, no matter what stats people might throw out there about how the New Big East might be comparable on the court, the national media perception is *strongly* in favor of the Catholic 7 (just as any stats pointing out deficiencies of ACC football compared to Big East football are ultimately irrelevant). However, going independent for UConn would be a football program killer. Now, if you get a Boise State-type offer from the MWC (and Cincinnati does, too), then it at least becomes a little bit more interesting to think about having football in the MWC and basketball in the C7 (even if I personally don't believe that would happen at all).