Taysom will start this Fall, and everyone knows it. Either one of those guys could blow the offense up this Spring/Summer and it wouldn't matter - the job would be Taysom's as soon as he healed. Taking starting reps through the offseason so that the offense works well when the star shows up again is NOT a D-I athlete's dream.
The writing is on the wall for QB's at BYU. The coaching staff is clearly behind Hill; after Hill is comes Mangum. It's really just a fight for second string, and that's not appealing to very many talented athletes. In football, there are few things more demeaning than a player getting "starting" reps when everyone (including teammates) knows the athlete isn't/won't be a starter. Hosick felt this way. Apparently, so did Olsen, Green, and Alex Kuresa. Good for them - I wish them well.
The QB race isn't open. There's just a minor gap where it would be convenient to the program (but not to the individual athletes) for there to be 1-2 backup QBs on hand.