The thing is, these conference tournaments are big money makers for that gets shared with lesser teams in the conference. I don't see how, say, a round of playoffs before the quarters (either the current format or a round of 16) makes more money for the SEC than a championship in ATL.
Someone suggested a "no harm" rule for losers in the conference championships. A win can boost you in, but a loss can't harm you vs at large teams. A loser gets the better of its post-Thanksgiving ranking or its post-championship ranking. It'd be weird for Alabama after that display last night, but probably good for VA.