I think this is an extremely weird take, that the Big 12 could be the aggressor here. They won't for a few reasons.
First of all, the PAC 12 currently has a minimum of six schools that are more attractive than the best Big 12 school. Washington, Oregon, Cal, Arizona State, Stanford, and Colorado are all more attractive to television executives because of their media markets and fanbases. Yes some of these schools don't fill up the stadium on game days, like Stanford, but their alumni base is one of the richest in the world - marketers pay a premium for demographics like that. The closest the Big 12 comes to matching that would either be a new school to the league, or Oklahoma State in football. Basketball isn't driving this bus, sorry Kansas.
The Big 12's remaining schools are usually pretty lucky if they have 750k fans watching on TV for a non OU or TX matchup - this is why those schools bolted so quickly - and there's not going to be any reason for TV executives to hand out a huge deal for the rights of those schools by and large. The Pac 12 has marginally better ratings and there is less dead weight - Baylor, TCU, and Kansas vs Wazzu and Oregon State. The Big 12 is also filled with commuter schools that aren't wealthy, big, or demographically sound. They aren't a factor in any big media markets either - they don't move the needle in Houston, Dallas, or Orlando - they're third or fourth in those markets at best.
In addition, the Pac12's TV contracts come up a year earlier. All of these schools are desperate for cash. This is a huge advantage right now. There is a good chance that Texas and Oklahoma buy themselves out or the league's membership criteria for enforcing damages to those schools end up precluding a big payout. In any case, schools aren't going to want to be the last man standing in that conference.