Who said that a single payer system would result in a level of pay for doctors and nurses that is unacceptable for them? It's not at all unusual for there to be structured pay scales in unionized and private businesses, and obviously it already exists in .gov jobs. It hasn't historically resulted in people having to work twice as hard for half the pay.
Regardless, the majority of countries that I'm aware of with single payer systems are not socialized (i.e. the hospitals are not owned by the fed, and physicians are not employees of the government)