Numbers, BYU was number one and it wasn’t even close. If any one of the four were the most desired, it was BYU. Even in the 90s when there were talks about BYU and New Mexico to the big 12, they didn’t do it because there “wasn’t another BYU.”
It probably had more to do with Texas and OU trying to squeeze more money out of ESPN than because there wasn’t a good #12.