Mandates is a pretty strong word. Maybe "requires" is more well-suited to the relationship between good quarterback play and a successful NFL franchise.
This topic was brought up time and time again on Jacksonville's local sports radio (BIG shoutout to the guys at SFR). And let me tell you, Jacksonville knows first-hand about the relationship between elite QB play and playoff berths (here's looking at you Garrard).
Look around the NFL, and you'll see how much water this "theory" holds.
Take the playoff teams for instance, starting with the championship teams.
The Vikings have some guy named Favre. The Saints have future HOF Drew Brees. The Colts? Some schmuck named Peyton. Even Mark Sanchez, the odd guy out, seems destined to be among the top 10-15 QBs in the league in the next three to five years, especially if he can hang on to that stellar defense.
Back it out further, to the divisional rounds.
Tony Romo? Pretty darn good. Kurt Warner? Future HOFer and two-time MVP. Joe Flacco? One of the most talented, not to mention gifted, young QBs in the league. Philip Rivers? Pro-bowler and arguably the best QB in the AFC.
Heck! Let's take it to the wild card round.
D-Nabb? HOFer. Carson Palmer? Heisman winner and Pro-bowler. Aaron Rodgers? Arguably the best QB in the NFC. Tom Brady? Are you kidding me?
And if that doesn't prove it, just check out the teams watching the playoffs at home and their QBs.
The Browns? Two-headed lethal (only to the health of Browns fans) combo of Quinn and Anderson. The Bills? Edwards and Fitzpatrick...blech! The Rams? The ever-injured Marc Bulger and some guy named Nall, or Null. I don't know.
Lastly, add in the bottom feeding teams with young, even rookie QBs: the Lions, Dolphins, Chiefs, Bucs, and Panthers.
Question: Which teams are the most hopeless? Are they the teams who have turned the reigns of their franchises over to young studs (i.e. the Lions or Fins)?
Nope! The hopeless, hapless ones are the teams that refuse to start over the right way with a QB, and who plug their hole at the position with a second-rate guy who would best be served in a backup role (COUGH...Jason Campbell...COUGH!).
I hate to say it, but the days of a middle-of-the road starting QB leading his team to the Super Bowl, a la Trent Dilfer or Kerry Collins, are over.