there is no present ownership by any church.

1 out of 13 schools is owned by a church, another 1 of the 13 schools is more conservative than the average university but has no present ownership from a church, and one school (which is a conference member for football only) is a military academy.

If BYU moves to the AAC for sporting reasons, then that would make sense.

But to make an argument that BYU should go to that conference for some-kumbaya bonding with other church schools and military academies is kind of a stretch.