Here is my reasoning: If Taysom wishes to play again then the ONLY place that is pretty much a 100% lock for him to start is BYU. Yes, he would likely win the QB race at many other places but the place that offers the best overall chance is BYU.
If Taysom wishes to play football again then would he not wish to play for a coach and a team that he has spent the last 4 years of his life with? He knows the people, he knows the system, he knows how it all works and his knowledge of the system will serve to make him as good as he can be. To go elsewhere is to start over with relationships with the coaches, the system and his teammates. He has to earn the trust of everyone all over again. Learn a new system, etc.
Would Taysom really like to go through the process of moving himself and his family for what? For a chance to play at a bigger program? Perhaps he never really fits into that program...If he stays here he knows what the status quo is and what is is is that he is a darkhorse heisman candidate with great relationships with his team and his coaches. Taysom may have stiff competition with Tanner but I would have to think that if the coaches intended to bench Taysom in favor of Tanner then they would let him know and he would move on. Therefore, If Taysom comes back we can assume he will start. If he starts his outlook and potential are unlikely to be much better no matter where he plays. So, why take the pain and the risk to go elsewhere?
IMO, the only logical choices are: A) Play 1 more year for BYU or B) move on from football altogether.
He could give the pros a try too I guess, but it seems unlikely he'd be given any serious looks with his history of injury. That may be a 3rd option worth some consideration but if I were him I would only take it if agents/NFL teams were giving me some serious interest prior to declaring myself eligible for the draft.

Anyway, that is just my opinion but I think Taysom would be unwise to go play for another college team.