Until someone makes a cogent argument that there is somebody from the pre-super bowl era that is better than Brady, I think it's fair to say GOAT in whatever context people want, but sure it could theoretically be a contradiction if someone only means post-Super Bowl era. Otto Graham certainly doesn't make the cut, considering his teams won in spite of him in a lot of cases. I think that alone would make Brady superior to him. If you've got another name, throw it out there. Y.A. Tittle? Norm Van Brocklin? George Blanda? Brady eviscerates these guys in virtually every category and every context.That is a contradiction, no? If you're going to talk about the greatest in the Super Bowl era, don't use the term “GOAT”.
Brady has more rushing yards than Graham, Tittle, Van Brocklin and Blanda. If you eliminate Blanda, Brady has more rushing yards than the other 3 combined. If you eliminate Graham, Brady has more than the other 3 combined. It's not even close. Those guys weren't asked to run much more than QB's are in today's game. Some of them did, but so does Cam Newton, Josh Allen and Russell Wilson, etc.I don't know. Maybe Brady is the greatest of all time -- one can certainly make a very strong case that he is. But while it's fair to ask this question "How well would Graham do in today's NFL?", it's also fair to ask "How well would Brady do in the 1950's NFL?" How do his stats look if the defenders are allowed to mug his receivers, and the defensive lineman can whack him on the head, and the coaches frequently ask the QB to run for yardage?
To answer your question, how would Brady do in the 1950's game? He'd dominate it. At 6'4, 225 pounds, he'd be one of the largest human beings on the field at any time, and probably be considered a pretty decent athlete by the standards of the time. Night Train Lane, who was one of the most feared defensive player of the time, was 6'1, 194 pounds. There were no 280lb defensive ends running 4.5-4.6 40's who were able to get to the quarterback in under 3 seconds. Chuck Bednarik was an absolute monster during the 1950's, he played center and linebacker (yes, center and linebacker) and he was only 6'3, 233lbs. And these are the exceptions. Most of the guys on the field back in those days would be small compared to a top tier high school program in America today.
On the flipside, at 6'1', guys like Sammy Baugh, and Graham and Van Brocklin were tall, All-American QB's. Drew Brees and Baker Mayfield are 6'1 and succeeding in today's game. Mayfield and Brees also have between 20-30 pounds on each of them. Guys today are just so, so much stronger and faster and physical, and the game is played at a speed that would have them dumbfounded.
It's kind of funny. In baseball, everyone discounts the guys from the turn of the century or before when having conversations about the GOAT in that sport, and in those cases, those guys stats dwarfed the guys in today's games (Cy Young anybody, Old Hoss Radbourne won 60 games and pitched over 600 innings in one season). We say it was a "different game" and we don't make qualifiers when talking about guys today by saying "Well, he's great, but he's nothing compared to Cy Young."
In football, when it comes to QB's, it's the opposite. The guys today are facing tougher competition, they are bigger, faster and stronger than ever before, they are playing in a much more balanced league and yet, the guys nowadays are putting up stats that dwarf the guys from the early days of the NFL, so what's the argument?
The reality is it's unfair to compare the guys that played in the 40's and 50's to the guys playing in today's game, and vice versa. Just like it's unfair to discount what Pedro did, because guys like Cy Young have numbers that make him look like a nobody.