Well I'd say it's better than a market where both are pretty opaque

There's too many points of negotiation between many, many entities for there to be transparent pricing in our current system.

A single payer system would eliminate those points and drive costs to their equilibrium point.

What do you mean? Aren’t we talking about the price of hospital visits, etc., meaning the performance/quality is expected to be good?

Medical care is not uniformly good. Your parent is alluding to a theoretical race to the bottom on quality.

There is a standard of quality one can expect that is defined by malpractice law.