The Patriots success has been the perfect storm of Brady (GREAT QB), Belichick (GREAT coach and de facto GM), and the AFC East (steaming pile).
Brady and Belichick are greatness, there's no denying that. But the Patriots also have the benefit of 6 games against awful competition every year, which helps get them first round byes and home field advantage (they're very average on the road in the playoffs). At home, they're tough to beat (true for most home playoff teams). And it certainly helps to have a QB that can pick apart a defense as well as Brady can.
Once they get to the Super Bowl, Belichick has two weeks to game plan and is a master of his craft.
Take Brady out of the equation = Belichick doesn't have as much success. Take Belichick out of the equation = Brady doesn't have as much success. Take them both and put them into a consistently competitive division = they don't get to 9 Super Bowls and certainly don't win 6.
Other teams can't replicate this because you need a great QB, a great coach, a great GM, and a weak division.