This is an interesting point, how much of the salary is determined by presumably impartial market forces, and how much of it is just status and social signalling.
We know status and social signalling play a significant role, otherwise behavioural economics and marketing wouldn't exist.
We also know that the diffrence between salaries of rank and file staff and C-suit executives have increased 15x in the past 20 years, without any corresponding increase in productivity
There is good reason to believe that if you could magically shove high-status men into nursing; nursing salaries would go up. But it's hard to see how it would happen unless we'd have equivalent of the draft for low status jobs.