Utah doesn't want to be in the Big 12 anyway so I don't think that'll happen.
As far as not playing each other anymore that ball is squarely in BYU's court. BYU has been the one has wanted to keep playing each other. We know Utah has wanted to stop playing BYU since they got in the Pac 12. Now that BYU doesn't need that game in football, I could see the "in-state game" going away in FB and MBB and maybe WBB too. I don't know how often they play each other in the other sports.