I think a lot of people underestimate the intelligence/football smarts factor that comes into the equation here with our complicated scheme and timing system.
That is precisely why many other good WRs around the league would not necessarily do well in N England.
We often see many good skills such as speed, size, strength, etc--but the actual truth of the matter is that Belichick is looking for something else too, due to some of the nuances of being able to succeed here in the system, and the way that everyone depends on each other to make the play work.
It's exactly the reason why we passed on Dez Bryant 3x over, and why many of the other WRs in the NFL probably aren't even considered here.
Braylon Edwards may be able to do okay in someone else's system, but I seriously doubt that he could pull this off here, and that is probably why Belichick would never even consider it.