I actually think Brady's skill set is sufficiently unique that most coaches would have miserably failed with him. I present the following:
* Brady wasn't immediately great - his first three years as a starter were good, better than most of us remember them (mid-80s QB rating back then was quality), but they weren't Tom Brady, the GOAT. He didn't break 7.0 YPA until 2004 (though 2003 was close), didn't break 250 YPG until 2005, didn't break a 90 QB rating until 2004; he was top-10, but not top-2.
* Brady lacked elite athletic ability; his strengths were pre-snap recognition, quickly progressing through reads, infrequent mistakes (there's a reason we remember the 4 Int games so well), and seemingly never losing his composure under pressure. Those are skills you need to build a scheme around, and frankly most coaches are either too stupid or too stubborn to adapt to a young QB.
* Bear in mind the competition: no matter how much the Patriots have dominated the AFC in the past decade and a half, there were always other would-be powerhouses: the Colts and Chargers, then Colts and Steelers, then the Ravens moving up, etc. Peyton is a good example of what happens when you burden a superior QB with inferior team building and good-to-poor coaching, and his skill set doesn't require anything special to build around.
If you put Brady onto a team like the Eagles - say they draft him late, and then McNabb goes down injured - then he collects a few rings, but if you put him on the Bengals, then he'd be mentioned alongside Marino as an all-time great who never won it all. The Browns would probably manage to ruin him entirely.
