Stallworth was signed before the Moss and Welker deals though, right? My recollection is that that was the first big move to fix the WR corps after '06. In any case point being though Moss was a trade (w/ a renegotiated contract) and Welker ultimately ended up being a trade (after a poison pill offer sheet as a RFA) I think those are tantamount to FA acquisitions. And those two transformed the WR position in NE for the next 4-6 years. Point being that you are absolutely right that since 2007 the Pats haven't had a bunch of success signing FA receivers, but part of that stretch is because there was really no reason for them to try. They still had both going into 2010, cut Moss in-season, went 14-2 anyway, and went into 2011 having the Gronk/AH thing going.
I think the more important distinction is between how NE straight-up drafts rookies vs. acquiring veterans. It's fair to say that they have struggled in the BB era to identify and draft the right WR prospects (besides Branch/Givens/Edelman...which is only 3 but it should be noted they have 5 SB rings between them and were a major part of each team). But since that's about a similar success rate in signing FAs and/or trading for veterans, I'm not sure what part of the process is breaking down, or if it really is breaking down at all. I think it's just a position where the failures are more obvious.
BB got Vrabel and Nink, for example, essentially off the trash heap that other teams didn't want. That's GREAT. Maybe we just don't spend that much time talking about all the DE/LBs he's signed that were underwhelming and washed out after a year or two. Part of the deal in why it becomes easy for some of us to praise BB despite some obvious "failures" is that almost all of these signings, at least initially, are done in a way that maximize opportunity if the player is good but minimize the damage if they're not. Lloyd is a good example - he wasn't exactly Megatron and he took **** for falling down...but overall the 2013 team would have been better for having him. For as great as Denver's O was that year, they won 13 games. NE won 12, ALL of them were close, Amendola played most of the year with that ripped groin, and we were lucky Edelman came to ball. Would have been nice to have another quality guy. Since we've been talking about HF advantage in a AFCCG, ya know.