Schedule/TV/Bowl Flexibility
8 year contract with ESPN (basically every game on national TV)
3rd-Tier TV rights
Ability to increase exposure/stretch fan base through national games
No contract worries (Sunday play, TV guarantees)
Will likely have access point to 4-team CFB playoff (at least better than pre-Indy)
You appear to be confusing conference membership with relevancy and while this is definitely a factor, it (and the other drawbacks of Independence), in my opinion, does not trump the perceived positives I listed above. And even if it did, I would remain faithful in my BYU fandom no matter what.