The truth is that QBs that get great results played on great teams. Casual fans put everything on the QB, but it's really not. To dominate teams need to be solid organizations with strong rosters top to bottom. Brady is no different. But using your logic, most of the great QBs go out the window too, making it kind of a meaningless argument.
Staubach had the Doomsday defense, great weapons and one of the most innovative coaches of his era. Aikman played on great teams top to bottom, set up by Jimmy Johnson's great coaching. The Montana-Young 49ers were mega-talented through the 80s to the mid 90s and ran an offense nobody had seen before. The 70s Steelers had an incredible talent stockpile and lots of anabolic steroids. The list goes on and on. You can find plenty of clunker games that the historically great QBs had that their teams won anyway. Hell, Peyton Manning's 2 playoff runs were both garbage statistically and relied on defense as much as anything. But nobody makes deep playoff runs without a good team around them in the first place.
The Patriots have been the ONLY post-2000 team to field strong teams and have elite coaching basically every single season. Of course they won more titles, they got more shots at the playoffs than anybody. No organization understands how the 21st century NFL works better than they do.
The thing about Brady is that everyone wants to credit "the system" - but nobody else can execute that system like he can, can they? Otherwise everyone in the NFL would just copy it and everything would be equal again. But of course that doesn't happen. So it's back to being about Brady again. I hesitate to call him "Literally Best of All Time" too, but he's up there for sure.