Every country with nationalized healthcare systems has lower wages for clinicians. So the notion that this wouldn't lower salaries is just ludicrous. That might be an acceptable trade-off but let's not pretend it doesn't exist.

In practice what we would see under a single-payer system is that many doctors would opt out and shift to a cash payment model. So the shortage of doctors would get even worse for patients who can't afford to pay out of pocket.