The Big 12 was simply a merger between the Big 8 and the SWC. UT and A&M were no brainers. Everybody else had flaws.
Houston probably would have been taken next, but they were on probation and falling apart. Tech, Baylor, TCU, SMU and Rice all were varying degrees of awful. There was no clear choice to get to 12.
Lt. Gov Bob Bullock has ideas. He went to both Tech and Baylor. He was the one who got consensus. BYU wasn't considered at all. BYU's name did come up when the Big 12 briefly considered expanding beyond 12.