I think your absolutely on to something but Kill and Beck desperately want this offense to be RPO based and so that why you see max being asked to pull and pop.
When Brady was most effective there was no RPO, he just got back to pass as quick as he could and had more than ample time and by the 2nd. half the KC defensive line was gassed. I would like to see on some plays Max do the same, no faking to a RB, drop back quick and deep, seeing the field as he goes back. Certainly Kenny and Beck see this also but will they implement it?