You need to take a step back from your narrative and really look at what you're saying.
I've said since that day that the team played differently with Taylor than they did with Peterman. I've said since that day that they looked like a different team. The problem with your narrative is that you don't place any of that on Peterman, saying instead that the team was only willing to play for Taylor.
So, I'll play your hypothetical within your narrative. But, I'm not going to go down the "Tom Brady" route. Instead, let's say we had Ryan Fitzpatrick back in the fold as our backup (that is, after all, what he is-- a career backup QB who will always be ready to take the reigns). It's week 11, against the Chargers, so he certainly has the playbook down, so there should be no excuses there. But, it is evident that the team is upset about the benching of Taylor. You're telling me that Fitz wouldn't have engaged the offense even before the game started to get them motivated to play? But, let's say that their poor attitude carries all the way over to the first offensive snap, and it is evident that the offense is not doing their jobs. Do you think that Fitz's leadership would have had no sway on that field? Do you think that Tom Brady's* leadership would have had no sway on that field?
The problem with your narrative is that you won't allow any of the blame for the performance of the offense to land on its on-field leader. If the offense, itself, were playing far worse under Nate Peterman than they were under Tyrod Taylor (and, they were. I was at Stubhub Stadium that day) how is that not a poor reflection on Nate Peterman? The five interceptions only tell half the story. The offense looked like a different team because Peterman did not have a command over the offense.
Well, the Patriots* better get rid of that bum, Tom Brady*. His 2017 completion percentage was only 66.3%.