This coaching fallacy is actually quite toxic in my experience... many/most people in the workplace don't want to change, and they don't want constructive criticism.
Every ineffective manager that I've ever known thinks that they can coach people into being more productive, better team members... but in the end those managers simply pat themselves on the back while the employee goes on causing headaches for the rest of the team.
That’s a dangerous generalization imo. There are absolutely organizations that value folks who are receptive to constructive criticism and who are willing to keep an open mind about all sorts of things. These companies screen carefully for characteristics that align with that culture and I can say from experience that it produces a much better working environment.
I do a lot of mentoring and coaching. Very roughly, 60% of people respond well, 30% struggle but have some improvement, and 10% don't respond at all. I really do think 90% of people benefit and change at least somewhat from coaching.
However, there is also a correalation between how difficult/toxic a team member is and how well they respond to coaching. At this point I think if a truly difficult team member responded to coaching, they probably would have stopped being difficult earlier in their career, because someone else would have told them to knock it off.
The only thing I've seen work there is being embedded into a culture that uniformally corrects the problematic behavior, and even that is a crapshoot.
However, that doesn't change my experience that most people do want to get better and do respond to help.
Every ineffective manager that I've ever known thinks that they can coach people into being more productive, better team members... but in the end those managers simply pat themselves on the back while the employee goes on causing headaches for the rest of the team.