I hate to derail this absolutely riveting discussion about what our coaches told us in high school, and how that relates to a play involving the best QB/receiver tandem in the game in the Super Bowl, but to me it seems possible that Belichick et al. felt that Welker:
(a) Might have made the Patriots a little to easy to game-plan when he is the first option on the field, in part because of how much Brady looks for him in the clutch;
(b) Might not be the best fit (compared to a top-tier outside threat) when Gronk and Hernandez are on the field;
(c) Is about to suffer a decline in playing ability.
These are really the only explanations I can think of that makes football sense.
I'm not sure any of these explanations are accurate.
A) Even if it did make the Pats "too easy to gameplan", the correct solution isn't geting rid of the player, the correct solution is changing your own gameplan to counteact this.
B) This doesn't seem to apply. The Pats didn't decide to replace Welker with a different type of reciever (outside threat). They replaced him with "Welker-lite".
C) Probably. The Pats seem to be fairly consistent in what they're willing to pay older players. I just think they're wrong this time. I don't see Welker's play declining within the next two years. And when you consider Brady only has a limited number of years left, himself, it makes this even more befuddling.