Hello! Kraft owns the team. If Brady wanted to stay, which he did, and Kraft did whatever he could to keep him, then the Patriots would have won the division for the 18th time in 19 seasons. Brady didn't void his contract either... what kind of a buffoonery comment is that?
Holy sh*t man, Mark Rypien? What are we doing here?
Did you read the criteria? I ask for any other quarterback in the history of the league who was a game manager yet won multiple Super Bowls and you give me Mark Rypien. A slob. Firstly, he won 1 Super Bowl, so you couldn't even get the multiple right. Secondly, he had more postseason turnovers than touchdowns. Brady had one less postseason win this year (4) alone then Rypien had in his entire career (5).
Doug Williams made for a nice episode of A Football Life but again he won 1 Super Bowl, where he had one magical quarter, otherwise he had a forgettable career and a postseason passer rating of 53.6, which is atrocious.
To your other points (regarding 2001-2003)...
Peyton Manning wasn't good in 2001, or really 2002, unless you think a quarterback can have a good season with 21 turnovers. He was co-MVP in 2003 but he ended Indy's season with 4 picks in the AFCCG. He was not better than Brady 2001-2003.
Brett Favre was a turnover machine most of his career. 2001-2003 he had 75 turnovers (in 53 games). I know that sounds made up but look it up, he actually did that. He was 2-3 in the postseasons with 11 turnovers (including a record 6 INT's in one game). So we can knock him off the list.
Kurt Warner had only 7 starts in 2002 and 2003 combined... he was 0-7 with 4 TD's and 12 INT's. Do I need to say anything else?
Rich Gannon 2001-2003 lost to Brady in a playoff game (2001) and set a Super Bowl record with 5 INT's (2002). He missed half of the 2003 season with a shoulder injury and wasn't any good in the games he played.
You failed.