If you put the Pats in a competitive division would they still have the success they have had the past decade. Sure early 2000's they were a legit contender, the past 5 years they have gotten in by default.
Divisions change. The AFC South used to be a joke except for the Colts for the longest time. The AFC West is currently the Broncos and a bunch of easy wins. The Vikings, Bears, and Lions all sucked at once for awhile, too. Same with the NFC West when the Rams were on top. The league is cyclical. It's not like a team can pick their division.
But for fun, let's see how the Patriots have fared in terms of SOS.
Patriots strength of schedule, 2007 - 2012
2007: #3 hardest (average opponents winning percentage: .539).
Only 2 teams with harder schedules: Raiders, Bills
Easiest schedule: Cardinals
2008: #32 hardest schedule, aka the easiest, aka the year Tom Brady went out with an ACL injury in the 1st quarter of game #1 (average opponents winning percentage: .387)
Second easiest: Chargers
2009: #3 hardest (average opponents winning percentage: .590)
Only 2 teams with harder schedules: Dolphins, Panthers
Easiest schedule: Bears
2010: #6 hardest (average opponents winning percentage: .531).
Notable teams with easier schedules that year: Giants, Ravens, Packers, Saints, Steelers, Broncos, 49ers, Colts, Bears
Easiest schedule: Cardinals
2011: #15 hardest (average opponents winning percentage: .504)
Notable teams with easier schedules that year: Eagles, Cowboys, Giants, Falcons, Bears, Steelers, 49ers, Ravens
2012: #32 hardest schedule (average opponents winning percentage: .453)
2nd easiest: Green Bay
3 out of the last 6 seasons they've had a top 6 hardest schedule, and 4 of the last 6 seasons they've hard a harder schedule than more than half the league.
So the facts don't support your conclusion that they have an annual cake walk. You're, once again, basing your analysis on the current news cycle. The Jets were good as short as 2 years ago, and Miami is on the rise. Divisional rivalries are more fun when the teams iare competitive, but that's hardly New England's fault.