Interesting idea, but would never work. You're basically eliminating the Utes from the schedule. They'd rather play in a PAC12 bowl tie-in, and you're eliminating any chance the Cougs have of playing anyone else in the post-season. With the way the bowl system works now, you have to get your tie-ins set up in advance. BYU is already set for bowls the next three years.
Now, if a playoff is instituted, then this idea may have more merit.
I do like the outside the box thinking though. What about moving the Utes to midway between the end of the regular season and bowl game? Both teams could use it as a bowl prep game. Regular season, two bye weeks, BYUvUtah, bye week, bowl game.