Take it for what it's worth (not a lot). I really only did the analysis and shared it to support the consensus is that BYU currently has significantly more talent in its two deep than UConn does.
Two words...religious affiliation.
We're the weird Mormon school, with the prohibitive honor code, owned by the socially conservative church that threw millions of dollars of resources into the passage of Prop 8 in California at the precisely the same time that socially liberal presidents of PAC10 schools in California started making their short lists of possible candidates for conference expansion.
BYU is also limited by church leadership and BYU's Board of Trustees who aren't necessarily "football guys". I believe BYU blew an opportunity to join the BIG12 in 2011.
I should state that while BYU lands its share of blue chip, nationally ranked Mormon recruits, we aren't consistently pulling in USC and Oregon type recruits (though, we did go head to head with USC, Oregon and Stanford and won Nick Kurtz, Devon Blackmon, and Uriah Leiataua this year). We recruit much better than a quirky church school located in the middle of the Rocky Mountain states has any business recruiting, but, I'm not asserting that we're a recruiting powerhouse by any stretch of the imagination.
I don't think it's any of the above. If you look at BYU's seasons going back to 2006, we are 11-2, 11-2, 10-3, 11-2, 7-6, 10-3, 8-5, and 8-5. We haven't had a breakout (undefeated or one loss) season for a few years, but we've won way more than our share of games since the turn of the century. I think, once again, BYU is the weird kid that others don't necessarily want to invite into their club. BYU has been consistently good since the late 1970's. I don't know what more, beyond another undefeated season, BYU has to do to gain entry into the club.