Price exists. Information that is embedded in the price, or, more precisely, in the myriad of market interactions that, among other things, also create the prices, however, is often lost. Or replaced with other information - e.g. who has a the better lobbyist or can negotiate with the government officials more efficiently. Also, it seems that you are implying there's a single "way it works in developed countries" - if you do, you are seriously mistaken, there are a wide variety of ways and each one has its own set of issues.

PP is referring to the price mechanism of markets. Not an arbitrary set price set by a regulator / central planner.

By definition if government runs a sector, there can be no pricing mechanism. Otherwise the government isn’t running it; it’s just a market.

The government is the payer, hospitals and doctors can still compete in pricing.

Plenty of US states have an effective duopoly of healthcare insurers, which is no different in effect from having a single payer.

The main difference is with for profit insurers, some % is skimmed off the top as profit instead of going into patient care.

He's probably referring to price controls, which basically everyone else has.

The US effectively has price controls by way of insurance company mandated charge books.