TL:DR Version - BYU has beaten 38% of P5 opponents over the last decade, being mediocre against lower-tier P5 teams, and very bad against good ones (though 3 of our 4 best wins have been recent). If we could either continue winning a touch more frequently against good (not great, NY6-type ones, but just those who are slightly above average or better) P5 teams or take care of business more consistently against bad ones, we'd be much more respected. ...Also, in looking at this, there's a truly absurd number of losses to Utah in the last decade, so we should probably do something about that.

Stats start here:
Over the last 10 years, we've won 38% of our games against P5 opponents (16/42), albeit mostly by beating up on bad P5 teams.

Over those 10 years we've played 23 P5 teams with a winning record vs other P5 opponents - against them we're winning 21% (5/23) with the wins being the ones we all endlessly brag on (plus GaTech)
2012 GaTech
2013 Texas
2018 Wisconsin
2019 Tennessee
2019 USC
(losses to 2011 Texas, 2011 Utah, 2012 Oregon St, 2012 Notre Dame, 2013 Wisconsin, 2013 Notre Dame, 2013 Washington, 2015 UCLA, 2015 Michigan, 2015 Utah, 2016 Utah, 2016 W Virginia, 2017 LSU, 2017 Wisconsin, 2017 Miss St, 2018 Washington, 2018 Utah, 2019 Utah)

Against the lesser P5 teams we've managed to win 11 of 19.
2011 Ole Miss (0-8 P5)
2012 Wash St (1-8 P5)
2013 GaTech (5-5 P5)
2014 Texas (5-6 P5)
2014 Virginia (4-6 P5)
2014 Cal (4-6 P5)
2015 Nebraska (4-7 P5)
2016 Arizona ( 1-8 P5)
2016 Mich St (2-8 P5)
2016 Miss St (3-5 P5)
2018 Arizona (4-5 P5)
(with losses to 2012 Utah, 2013 Virginia, 2013 Utah, 2015 Mizzou, 2016 UCLA, 2017 Utah, 2018 Cal, 2019 Washington)

Moral of the story: BYU is, over the last decade, relatively comparable to a bad P5 team. This is similarly true about the AAC in general - they are able to get a fair number of P5 wins against lower level P5s, but have a terrible record against better ones. BYU is probably comparable over the last decade to some of the better teams in the AAC (UCF, Memphis, Cincy, Houston) and would match up well in the AAC. Travel would be difficult, but especially if BYU was brought-in football only (to complement Wichita St which is everything but football) this would be less of an issue and win/win for both BYU and the conference.