I think it’s largely because of his history as a player.
He wasn’t great for ages and people felt he was the beneficiary of undue favouritism from SAF. People don’t like changing their minds, were resentful when he became good, and rejoice in again having something to berate him for.
I don’t recall Nicky Butt getting the same stick while he was in the job prior to Fletcher. In his case I think scepticism was more deserved, as the role was created for him after he’d been sacked as head of the Academy, and looked like it was largely ceremonial. The fact that when he left they recruited Fletcher as his replacement suggests that it was actually a real job. If it wasn’t surely the role would have lapsed on Butt’s departure?