Who wouldn't want to play in a conference named the Big Privates?I'm assuming that TCU will have the option of being part of a regional conference (remains of the Big 12), and that key relationships for that are in place. So I would think about what else might be worth pursuing.
I'd be interested to know what Stanford has as its plan B. (Plan A is trying to hitch a ride with Cal if the Bears can successfully use legislators to tether themselves to UCLA. Could happen, and I think Stanford's strength in minor sports would appeal to the B1G.)
Then, I'd be trying to figure out what Notre Dame is thinking (probably time for them to go to B1G; they need a home for non-football sports).
Then, I'd try to learn the likelihood of Northwestern and Vandy being offloaded from the superconferences, and find out what Miami and Duke are looking at if the ACC is torn up.
All that to say, it could be worth exploring the idea of a national football-playing selective privates conference. Except for Notre Dame, it would have no big media audience even with presence in good markets, but from a recruiting standpoint, there will always be a group of athletes for which selective private schools have appeal, and running with that crowd would be good for TCU's academic reputation. A core of Notre Dame, Stanford, Miami, TCU, Vandy, Baylor & Duke would be exceptional in minor sports, salty in men's basketball, and solid in football. Could fill out with Northwestern, Wake or selective ACC state schools that would be homeless. I could see a group like that wanting to exit the arms race while still keeping a commitment to D1 sports excellence. And a slightly higher academic requirement could be installed across the board.
High travel costs, but you could set up pods to limit some of the travel--say, (Duke-Wake-UVa-UNC-Ga Tech-Miami) (TCU-Baylor-SMU-Vandy-Tulane-Rice) (Notre Dame-Northwestern-Stanford-Cal-Washington/Air Force/BYU).
Is that better than a Big 12 that adds some of the PAC leftovers? Probably not, but I would be having those conversations.