This is a good discussion and it sucks that I'm late to it, but not to cop out, but I think it's both. Some QBs are successful by nature and some are by nurture. And I think a lot of it depends on which positive traits (and how much in the positive) the QB has. And I guess that also means how well the strength of the offensive coaching fits to the QB.
Like we praise Andy Reid and Kyle Shanahan, but Reid couldn't get over the hump with McNabb or Alex Smith. He made them better, but not good enough. Shanahan couldn't do anything with the most moldable, 20-year old, QB in the world at the time, but is a SB favorite with the equivalent of D1 Tyson Bagent, who was picked 1 slot ahead of the UDFAs.
But a lot is finding a way to get the most out of what a QB naturally does well, while minimizing the need for the QB to be put in positions to have to do things he doesn't do well too often. Also, I think you should NOT spend much time trying to correct what a QB doesn't do well to fit in your scheme. With Fields in particular, you have an OC who wants to throw quick to playmakers potentially in small windows, while you have a QB that wants things to open up down the field. I think Getsy did a good job of calling to Fields' strengths the previous 2 weeks, but it's pretty hard to do when the other team is sending more guys than you can block in front of him. And obviously, Fields' weaknesses mean he can't make the adjustments necessary to combat that, which seems to be his fatal flaw that takes him off of this team.
But you also can't consistently run an offense to your QBs strength that likes to hold onto the ball if you have below average OL talent and WRs who can't separate. Then you throw on injuries on top of that and it's been a disaster for 2 years between getting the most out of Fields and the most out of the offense. And that part is not on him. Poles scouted him in college. There was every indication there he liked to hold onto the ball and they put him in a terrible situation to succeed almost intentionally.
And if you think Fields likes to hold onto the ball too long, Caleb Williams has the record for time to throw since it's been calculated. He does seem to have enough of that Mahomes ability to adapt and get the ball out quickly when he needs to or the situation dictates it, but you never know until you put him in that situation. And if you put him behind remedial centers, a bottom 10 LT and you have injury prone players at both guard spots, you're going to find out in a hurry if he can overcome his negative traits well enough.