Most of this attached post isn't relevant to the discussion, but compare BYUs numbers/success over the end of their time in the MWC and their time in Independence.
BYU won at a higher rate against both G5 and P5 opponents while in the mountain west. They were more consistently ranked. They had more players drafted
https://www.cougarboard.com/board/message.html?id=26299183
I'm not saying all those things are the result of independence vs G5 affiliation, but they all did happen