It makes no sense at all for UConn to accept a non-football offer. Keep in mind, it wouldn't be "basketball only." It would be everything that the Big 12 has other than football.
The Big East isn't perfect, but neither is the Big 12. The Big East is just as good as the Big 12 in basketball and many other sports it plays. The only reasons to join the Big 12: i) money, and that money is only a big enough difference with football; and ii) quality football schedule and bowl access. Number (ii) is a bit of a strawman. This is all about money.