So many UConn fans were indifferent to being in the AAC not only for lack of big name opponents but also because the AAC was viewed as being outside the P5 for football or P6 for basketball. You knew you were viewed as being minor league. There were top 25 games against football teams and the AAC put football teams in the CFP or whatever iteration it was at the time- and UConn fans didn't care. Basketball played games against Top 25 teams but other than Cincy, Houston and Memphis, no one cared.
The benefit of going to the Big12 is the Big12 is part of the "club". They're in the in the crowd and gets coverage across the nation as such.
Also, being in the Big12 makes it even easier, as a 5-time national champion, to schedule more big time out of conference games and be part of big time tourneys, MTE's and home and home OOC games. The overall schedule will be better for hoops. I'm not more excited about playing TCU in hoops than I am DePaul. Every conference is going to have some games which just don't get the juices flowing.
Football is going to get crushed for a while since it takes longer to increase the talent needed to compete week in and week out but they will be playing a bunch of good teams.
I think I'm most excited for Penders and the baseball program who get absolutely crushed by the crappy quality of the BE conference for baseball. That guy has the sweat equity in the university and program and deserves a bigger a national stage to showcase his talents.
track and field and volleyball should get big upticks in competition and talent too.
I can't think of a single program whose profile will be harmed.
You do it.