Regarding Edelman specifically, I basically look at this past offensive season with an asterisk, due to some of the reasons that you provided. There's no doubt that Edelman's production had a lot to do with no other viable options, and the injury and rookie factors as well. I think we'll get a much better read on Belichick's feelings re: Edelman if/when some numbers start to get leaked in terms of Patriot offers.
I wouldn't think that Belichick is going to offer anything close to what some are projecting myself, so I think unless Edelman is willing to take a conservative deal where he would leave money from another team on the table, he'll be gone. Just my opinion though. It's hard to guess what Belichick is thinking, but I'd be a bit surprised if he chose to pay Edelman more than about 4.5m AAV--tops.
i think that no one offers Edelman more than that 4.5 mill, and maybe not more than 3/10.
Edelman did a great job this year. He does a great job running after the catch. He played in an offense where, aside from him:
The #1 target was injured for half the season
The #2 target, who relies on quick breaks in and out of cuts was nursing a groin injury all season.
The #3 target was incarcerated.
The #3 target to replace him missed half the season with a broken wrist.
The outside receivers were all injured for numerous games, the best of which was hampered through camp and slow to develop a chemistry with Brady.
The "Edelman-centrc" Patriot offense was the least productive Patriot offense in years. That is not Edelmans fault, it is an indication that his production was out of necessity not design.
Scoring was down a TD a game from 13 and 5-7 points from each of the last 3 seasons. Scoring in games without Gronk was down more than 10 points a game from last year.
Teams don't pay big money to a player who steps in and gets catches while the offense takes a step backward.
As far as the 'system' I'm not sure why the term system player got into this, but the point at hand is that the system the Patriots run puts heavy emphasis on short, quick passes, ad running quick players through traffic to get them open. That philosophy played into edlemans production, and in a different system his skillset would not be as valued.