Kelly's offense works best with a dual threat QB like Dan Lefevour or Zach Collaros. Golson can run, but in watching him, you sort of get the feeling he doesn't really want to (he doesn't really seem to have the desire and feel of a runner). In contrast, Zaire seems to want the ball in his hands, and wants to run. Would Golson call his own number and run a QB iso on 4th and 3? Highly doubtful.
I know Kelly has made due with passing QBs in the past like Tony Pike and Tommy Rees, but I truly believe to have a chance to beat an elite Ohio St. or Alabama type team, he would need a very dynamic dual threat QB.
Should Golson transfer, I think he would have a lot of opportunities. To remain at Notre Dame would mean he would continue to be a square peg in a round hole.