I think the 12 team playoff means there is no reason for Boise St. or BYU to join the AAC. Why? First, Boise has a better chance of winning the MWC than the AAC so they could go 13-0, win the MWC, and they would probably be the higher ranked conference champ over a 12-1 AAC team. For BYU, they are playing 7 P5 schools in 2021 (Arizona, Utah, Arizona St., Baylor, Washington St., Virginia, and USC) as well as Boise St., Utah St. and USF so if they go 12-1 with that schedule they would be ranked in the top 12 and probably get a playoff bid. BYU can schedule decent schools, so why go to the AAC?
Going back to 2010 and using the final BCS or CFP rankings, the AAC (teams currently in the AAC) was the highest ranked G5 champion 6 times, the MWC 3x, and the MAC 2x.