The analysis you present is not uncommon, where the businessman somehow gets to choose how much money he makes in a vacuum, a situation that doesn't really exist.
Ironically, lots of US regulations prevent providers from entering markets, letting providers that already have regulatory approval charge more. Some regulations are literally written with this as the goal (CONs, Medicare reimbursement rules designed to prop up small hospitals with emergency rooms).
It would be just as massive an overhaul to turn this sector into a truly competitive market as it would be to nationalize it.
Absolutely no one anywhere is suggesting doctors and nurses should work for free. Single payer advocates are only suggesting that we cut out the byzantine mechanism of the US medical billing regime, and let the American people pay health care professionals directly, with taxes, instead.
And good compensation for health professionals can happen in a non-profit context too.
Compare to an free or open source project. A project that pays some contributors, but not others is a rather unhealthy situation. Such a project would have more difficulties attracting and retaining developers.
Don't underestimate what people will do for other than financial compensation, given suitable conditions.