I definitely don't want to underappreciate Bill, or undersell what he's done for the Patriots. It does seem clear to me, though, that he really isn't very good when it comes to offense. Having Brady and a decent-to-solid O-line resulted in quite a few receivers looking better than they actually were—not that they were bad, but several of them produced a lot less before and after they were with the Patriots.
Basically, I'm fine with Bill staying on if he's just the coach and not the GM. Well, I'd be fine with him giving draft input on defensive players, because he's picked quite a few really good defensive players, even in recent years (Barmore, Gonzalez), but he seems to have very little talent for evaluating receivers, and his failure to sufficiently address the O-line over the last couple years is a big issue. I think Mac Jones, as he demonstrated in his rookie season, could've been at least a decent QB for this team, but Bill's failure with the O-line and his completely ridiculous decision to have defensive coaches run the offense last season have ruined Mac for this team, thus setting back the rebuild by at least two full seasons.