Prescott said 'Sanchez taught him the most'. I don't want to discount that loving act too much, but that isn't his job. His full-time job is to be ready to step in and win that week's game. I've never heard of a team signing a QB to play backup and coach. If you have some sources that say different, post us a link, and I'll check it out.
Like I said, conventional wisdom is Shaw is safe on PS, but Fales didn't do as well as Shaw, and Bears had to bring him into the 53-roster to keep NE from taking him. I don't think you usually get a 'warning'. My main point is I'd rather develop & play Shaw than Sanchez as my backup. I haven't any argument why the opposite is better.