A "free market" is an idealist concept for something that can not exist in the real world under capitalism. In a system where resources are distributed based on capital, and resources themselves are capital, oligopolies and monopolies are logically inevitable and the market is never a level playing field.

The reality is that many goods and services have poor elasticity or are inelastic. A "free market" completely falls apart when it meets such variables. This includes healthcare – there is no economic incentive for the owning class to keep prices as low as possible, as people need healthcare and many times people will die without it. The way to make the most profit in that situation is for businesses in an area to simply make prices as high as legally possible and bury patients in debt, or for businesses to collaborate on price, etc.

This is doubly true when considering that people often don't have a choice as to where they go to receive healthcare in many scenarios, there is no "just go to a different hospital" or "just get an ambulance from a different provider" or even "stop going to the only doctor in your area and instead drive 2 hours away whenever you want to go see one, and you have to have a car to do that". So even in the completely unrealistic fake scenario that healthcare providers would otherwise have an incentive to "compete" on lowering price, this fact alone almost completely topples that. There is little to no choice a majority of the time.

People like to think of a "free market" but in real life the most profitable thing to do often times isn't a good outcome for consumers. Just look how fucked up privatized rail caused transport in the US to be. And look at the healthcare system... which has sucked ever since it was a market. And look at the parking meters in Chicago. The complete and utter failure of those systems isn't caused by "we regulate it too much". Public services becoming private just causes them to become anti-consumer.

This isn't healthcare-exclusive, but healthcare is so important and the system is so abusable that it must be owned by the public for society to be functional. A system where basic necessities aren't commoditized is the only solution to make sure people have free access to basic necessities.

Also you fail to consider that monopolies and oligopolies come from somewhere. That somewhere is the "free market". They didn't just spontaneously pop into existence because of big government or whatever, they came into existence because of the lack of regulation and still exist because of there being extremely poor regulation. It is just a fact of the capitalist free market that people with more capital than others have the capacity to gain more capital, and people with less capital are prone to lose capital. There is no system that isn't heavily regulated that consistently prevents a minority of entities in a market from accumulating a majority of resources over time. Corporatism emerges from free markets, and there is no solution short of extreme regulation for the problem (although the ideal solution is to just publicize all necessities and services important to the general population outright)