There is absolutely zero point to giving Minshew any burn once they bench Jacoby. None. At that point, the season is all about the future and you need to see what Beck has and give him enough time to get whiplash from his first couple starts and then see if he’s able to figure the game out in Q4.
Just dumping him into Q4 of the season is completely pointless. The team will have given up by then, guys will start playing for paychecks above all else (if they’re even still playing and not shelving themselves on IR) and he’ll have almost zero time to adjust to the NFL game and see if he’s got any goods.