Brady absolutely was a game manager from 2001 to 2006. Then he got Moss and started throwing it to him in triple coverage and turned into a different QB. He's been great from that point forth in my opinion. Before 2007, he won games because he had a great defense, a running game, great coaching, and a kicker that just wouldn't miss. He would dink and dunk you to death. It used to drive me nuts. He morphed into a QB that could beat you consistently with his arm.
I'm not sure I ever considered Montana a game manager but he definitely was clutch and also benefited from great defenses, a running game, and great coaching.
It's hard for me to call guys like Montana or Brady (early in his career) the "best of all time" for that very reason. Their lives have been made so much easier because of the teams around them. I assure you that just removing Vinatieri from the Patriots would've resulted in less Super Bowl wins and appearances!! Meanwhile Marino, Manning, or Rodgers consistently put up great numbers on terrible teams and kept them in contention.
Just imagine Marino with a great defense, strong running game, and clutch kicking on a yearly basis.