Will be even more lame if BYU tries to big-time Utah after joining a depleted Big XII. I think we should be grateful that the Hateful Eight + the G5 wallflowers is still considered a P5 conference, and should remain humble instead of trying to flex. The CFB landscape is very much in flux, and teams like BYU will really benefit from friends when the landscape shifts again.
Realistically, wins over Utah, Boise State, and Utah State are going to do more for BYU recruiting than games in Eastern Time (even holding aside BYU's terrible record in that time zone). Even if BYU actually has a "national" following, they have a recruiting base that is very regional and it's a good thing if BYU regularly wins the regional head-to-head games.