Just my opinion, but having watched these Bama teams over Saban's tenure, it seems that despite the offensive philosophy, the one thing that dictates offensive success during a game has been whether or not the team wins on first down. Winning would be gaining 5+ yards on first down. It sure seems to me that if Bama can't win on first down, the offense almost throws away second down by going to a predictable play call and setting up a long third down, which over Saban's tenure, Bama has not converted at a high rate.
I know that when Blake Sims was the QB, his legs, and the freedom to run the QB if needed, helped the team avoid losses on plays that fell apart. So I don't know if going to a strictly drop back passer would be beneficial. I also don't think that asking Hurts or whomever else is the QB to stay in the pocket and deliver the ball, even with the pocket collapsing, is too much to ask either.