Let's say Maye starts and plays really poorly. The veteran players on the team are looking to be put in position to succeed as much as possible. They're going to be looking at the coach to pull the guy who's playing poorly and give someone else a shot, Jacoby Brissett in this case. No different than they would at any other position. They're loyal to their own careers and earning potential before the long term development of the franchise.
It's much smoother and easier to justify to the locker room if you play the vet, he sucks, and then you go to the rookie. Even if Maye plays terrible then, all of the vets will understand that Brissett wouldn't give them any better a chance to win and they'll accept Maye's struggles.