It's weird to me for you to write "Brady would have failed in Cleveland" as a point for Belichick when Belichick actually did fail in Cleveland, in part because of circumstances beyond his control, but in large part because he couldn't find a quarterback. The Patriots went 5-13 with Bledsoe and finished finishing 25th in points in 2000 (they haven't finished worse than 12th with Brady).
Ugh, I hate even typing the preceding paragraph because it sounds like crapping on Belichick, which is the last thing I want to do.
To me this sounds like as much Brady helping Belichick as Belichick helping Brady. The feedback helps Brady, sure, but by needling Brady in front of the other members of the team, it forces everyone to fall in line because the star is. Red Auerbach used to do this to Bill Russell, too, criticizing him in front of the team (sometimes for fabricated stuff) to send a message not to Russell but to the rest of the squad. Some QBs wouldn't put up with this. Ben Roethlisberger just got his OC fired, for instance.
This article is great and hammers home how Brady is special in this regard:
https://www.si.com/mmqb/2017/01/18/nfl-tom-brady-bill-belichick-new-england-patriots
Would Bledsoe take this kind of coaching? Would Manning? To me, this is just another way in which Brady is special.