The problem was that none of the schools had 8 votes, including byu. The Big12 is so dysfunctional they couldn't reach a compromise.
Texas likely dug its heals in on Houston which killed any possibility since the non Texas schools didn't want Houston. Byu didn't have 8 votes due to social issues and religion.
They didn't vote on any teams because they knew none had 8 votes, let alone two. Several teams just switched to a no expansion stance once it was clear they couldn't get their favorite to 8, namely Texas and Oklahoma who will have options plenty come 2024