I've admittedly never been part of any $1B Private Equity NCAA Conference whatever deals. But, I'm fairly certain the plan would be to invest short term for the potential long term ROI. So, sure why not, I'll take a crack at it...
First of all, A&M, Penn State, Oregon, Clemson and FSU are NOT blue bloods. So, let's set them aside for a minute.
In its simplest form, let's just say all it would take is adding 2 blue bloods to get Fox/ESPN/Netflix/Amazon/whoever to increase the Big 12's TV deal equal to the SEC or BIG. You've got a half Billion dollar signing bonus each to go find two. Hey, (fill in the blank) blue blood...here's $500 Million and a guaranteed X number of years TV deal equal to what you've got now. Interested?
In that way too overly dumbed down scenario, you tell me which blue blood wouldn't make that move.
It would obviously be much more complex than that, but I just laid that out for illustration purposes. The TV network would require much more than just 2 teams, so insert the fringe blue bloods like the ones you listed above. The Allstate 12 would need to figure out if $1B could get the TV guys what they wanted. And the PE would have to determine if that $1B would result in a decent ROI if all of that happened. Again, I'm oversimplifying for sure.
Maybe I've just watched too much 'Welcome to Wrexham' but it seems like the same general concept to me. Hell, maybe the Allstate 12 will get a reality series documenting the process as part of the deal