I think he would have made it and won the Super Bowl that year if it wasn't for the injury. 15 seasons in the league is nothing to sneeze at. Congrats and good luck to him.
A good example of how a little good luck or bad luck (including injuries) can make a difference in how a career is perceived. He's in the second group with Eli, Roethlisberger, Rivers, and Ryan, below the top group of Peyton, Brady, Brees, and Rodgers, of accomplished recent QBs with 10+ years in the league, but no Super Bowl appearances for him and Rivers means they are viewed differently from all of the others (and no wins for Ryan means he's not viewed the same as Super Bowl winners as well).
You are correct, his cap hit is 16 plus million but not his actual base salary of 11 million. Still not chump change.
I'd put him in the 3rd tier with Flacco, Alex Smith and a few others. All those names in the 2nd tier you mentioned plus Wilson and Newton are better than Palmer. I do agree that the injury in his rookie year or 2nd year in the playoffs against the Steelers really changed his career trajectory.
I think he's far better than Flacco and Smith, and probably better than Wilson and Newton, too, although they weren't eligible for my list of QBs with 10+ years in the league. He is 12th in NFL history in career passing yards, 12th in career passing TDs, and 11th in career game-winning drives; every player ahead of him is either in the Hall of Fame or a slam dunk for the Hall of Fame, other than perhaps Eli, Rivers, and him, which is exactly my point. He's also 13th in career passing yards per game and 19th in career completion percentage. The fact that people don't realize just how good Palmer and Rivers have been through their entire careers is purely because of the lack of playoff recognition in general and Super Bowl recognition in particular, and also because of playing in the west so they're playing far fewer 1 PM games than people like Eli.
He was never the same after the injury against Pitt in the 2005 playoffs. IMO, he was on pace to be a hall of famer before the injury. Still had a good career.