How? Be specific.
The health care providers are by law and by oath required to provide services first in the case of a life threatening illness, and inquire about cost second. How do you run a profitable business when you are required to provide your services before you can enquire about cost?
You're holding up Capitalism as some sort of magic cure all totem. Free Markets work for a lot of things, but Health Care is not one of them. The costs associated with maintaining and keeping a sterile environment, the fact services have to be provided even to those who can not pay, and the fact that in a health emergency financial considerations do not enter play until after a patient is stabilized means that a free market system won't work. There's a reason that communities often have to finance local hospitals if they want to have them. Free market systems are fine, but they don't address all the issues here.
Well you're only looking at life threatening emergencies without taking into account minor surgeries and the like, where the patient and the doctor are able to discuss the price of a procedure. However, if costs are lowered then more people would be able to pay for the treatment, even if it is a major surgery. It might still be difficult but it wouldn't be completely impossible and wouldn't force as many people into bankruptcy. Then of course most people do have insurance and insurance rates would drop as the price of different procedures and medications drop, and if people were able to pay out of pocket for smaller surgeries and annual check ups the price would drop even further. This means more people would have insurance for emergencies.
The problem is *how* are the costs going to be lowered. For non-life threatening situations responsible folks do discuss cost and take that into account.
You still have to explain how a totally free market system for healthcare will even be possible, much less how it will lower costs. Again, in a rural community your selection of doctors and hospitals is extremely limited. IF you're in a larger urban community you may have some freedom to shop around, but even that is questionable. Frequently hospitals specialize quickly even in a metropolitan area due to the cost of maintaining up to date treatment wards.
In the rural community you have *zero* chance of even starting a free market competitiion. How can you even have captialism when services are provided by a single individual. The argument for free market health care falls apart once you get into the life threatening conditions, but even setting it aside there's still problems applying the principles of Capitalism to the "optional" services in the health care field.
I do think Capitalism works in a lot of cases. This isn't one of them.