The rate at which new doctors are trained in the USA has historically been bottlenecked by the number of residency program slots available. Hospitals financially benefit from each resident they employ, but not as much as they do from adding other roles, instead (such as nurses). Also, it is not trivial to create a new residency program or expand an existing one (accreditation requirements, other fixed costs, etc.). This is why 25 % of USA physicians are immigrants. The Republicans have also made it more expensive to get loans for medical school, which will discourage some people from going to med school in the future, although the insufficient supply of residency slots might still end up being the bottleneck.

But even if we did not increase the supply of doctors, moving to Single Payer would still benefit us by reducing cost. I don't think Single Payer would need to be coupled to increasing the supply of physicians.