Fields just isn't accurate at all, there's only so much you can coach up. With better coaching he could improve his vision and pocket presence, but he's still missing some key components that will keep him away from becoming a franchise QB.
I noticed similar things with Marcus Mariota, he got plugged into some bad offenses in Tennessee and got a second shot in Atlanta with the best OL and weapons (Pitts was coming off a 1000 yard rookie year) he'd ever had, yet he still played like a bust and eventually got benched. And while their coaching isn't the cream of the crop, Mariota got his chances and failed.
Even the best QB coach there is, Kyle Shanahan, gave up on a ultra-talented QB prospect in Trey Lance for a wimpy 4th round pick. There are limits to how much coaching can fix.
Pittsburgh's defense has mostly been responsible for the wins, as their passing game has been atrocious. Bad enough that they just fired a coach mid-season for the first time since 1941. Belichick's defense hasn't been as good, and they also don't have a run game like Pittsburgh does.
I do think Jones could be a low-end starter as we saw flashes of that in his rookie year, but he's been coached by the likes of Matt Patricia and Bill O'Brien...