Would you risk anyone snagging him up, though ? And giving him a case of the foxboro flu is also dangerous unless you keep one of the designated spots open for him specifically because if Brady or JG sustain an injury then anyone coming of the street wont be as good as JB with respect to the system.
I honestly don't know.
For me, it comes down to the total number of reasonably viable pass-catchers on the roster.
Based on a breakdown of previous (+/-) 600 passing attempt seasons, my original target distribution projection was:
Tier-1: Gronk/Cooks/Edelman = ~95-100 targets each
Tier-2: White/Hogan/Mitchell* = ~65-70 targets each
Tier-3: Lewis/Allen/Burkhead/Amendola split the vast majority of the ~100-120 remaining targets among them.
Tier-4: Gillislee/Develin/a TE-3/Slater pick up a handful of targets each.
With Edelman gone (and *Mitchell dinged up, and Slater possibly gone), I don't think the target redistribution required to compensate for Edelman's loss is a matter of (A) simply promoting one guy from each Tier to the next Tier up in terms of number of targets, or (B) simply dividing Edelman's targets among the remaining guys proportionate to their Tier. At some point, one or more of the Tier-1/Tier-2/Tier-3 guys are likely to miss a game (or two or three), and further adjustments to compensate could limit the available playbook for those games/opponents.
Brissett taking up a roster spot certainly reduces the Pats' flexibility in retaining other supplemental pass-catchers.
So, it's potentially losing Brissett versus ensuring that the playbook isn't limited for Brady/JG at some point later in the season for a couple games, perhaps critical ones.
I just haven't decided yet which represents the greater downside and which provides more insurance.