I will stipulate that there were many problems on the team.

However,

Brees had full authority and license to call plays and/or change plays at the line. Some of the "abandoning the run" falls to him, as does misreading defenses and calling plays that fail.

15 of 19 interceptions were his bad throws or bad decisions, the others bad luck. The 4 pick-6s were all unforced errors, and each were fatal in those games.

Not that QBR is the end-all of performance metrics, but:

2011 - 1 game under 50, 3 total games under 70 (2 of 3 losses), averaging 84.0 (2nd)
2012 - 7 games under 50 (all losses), averaging 67.9 (9th)

Pretty clear, if he doesn't play like the highest paid player in the league, Saints don't win. For almost half the season, he didn't crack the top 25 best QBs.

You sink that much resource into one guy, he better deliver, no excuses.