I'm in an odd spot since I have rooting interests for both Utah and BYU and I can tell you that the general view among Utah fans is that BYU went Independent basically in response to Utah getting picked up for the PAC12.

And that's not just Utah fans - read articles at the time (from non-BYU, non-Utah sources) and the primary arguments seem to be either

1. This is a knee-jerk reaction to Utah getting a great opportunity and BYU needing to do something, anything (frankly I think there's some truth to this, though they've done well with it since then)
or
2. This is motivated by the chance to increase publicity for the LDS church

"The decision to go independent had to be ratified by church leaders, and I’m sure publicity was a factor in the decision. With a recent media campaign aimed at showing that Mormons are in fact normal, this move makes total sense. So who really cares about a championship? Sure a crystal ball is nice to have, but it is usually passed around between the have’s, and held out of reach from the have not’s. Relegating themselves to Army/Navy-like BCS potential may even push the ball further away, but pushing BYU football and the LDS faith across America is what is important to this university and that’s what independence will do."

Either way, it was generally accepted/viewed as a poor decision for purposes of being competitive in football and allowing Utah to get further ahead.

Bottom Line: BYU has been relegated to the little-brother role since 2011 and declaring Independence didn't change it - if anything, it reinforced it. That said, joining the AAC gives BYU a chance to reverse that narrative as they might have an easier path to the playoff than Utah does.