I have never heard anyone use that argument before.
I dont recall ever hearing even from the far right that the reasons for high medical costs in America is not due to closed markets allowing companies to monopolized/limit competition allowing them to drive up prices. Which could be taken care of if a free market is created allowing all insurance companies into all markets to compete to drive prices down.
As is, right now. You get a few options for insurance in your area. Say you need an X-ray. Which ever insurance you have is only covered by a portion of the providers and so most providers unify their prices since there is no competition and thus, an x-ray is going to cost about the same everywhere.
Kick that market open. Allow every single insurance company to insure anyone, anywhere...suddenly 100s of companies are trying to get you as their customer and their coverage prices drop to do it. Now the medical service market is suddenly kicked open also, they will have to accept all providers since anyone can be covered by any company (no longer limited to a few choices)...now, suddenly needing an x-ray is vastly different as you can now visit ANYPLACE that does x-rays since they will accept your insurance.
What will that do to prices? lower them. Because you will no longer be FORCED to get an x-ray at certain places like before and now they will need an incentive to make you choose them out of the many choices available to you.
Problem solved. No need for socialized anything. No need for new regulations. No need for more convoluted laws or market controls.