There's a difference between "shouldn't have a price" and "doesn't have value". Nobody says a doctor can't get paid - but what most people outside the USA has realized is that it's tantamount to murder to demand that sick people need money to be allowed treatment, to give insurance companies the power to deny a life-saving claim under ANY circumstances.
What most countries outside the USA has done to address this is institute single-payer universal healthcare. And apparently this is one case which absolutely disproves the claims of free-market fundamentalists because these "socialist" (as they are called by Americans who don't know what the word means) medical systems are MUCH higher quality than your for-profit model (the USA's healthcare industry isn't even in the top-10 -it's number 37 worldwide) and tellingly the most vulnerable people in society show the greatest benefit (for example - they all have far lower child-mortality rates) and worst of all - they all manage to do so while spending FAR less money in total on health-care than you do.
When you DO in fact get better quality, for a lower total cost, from sharing the cost through taxes, that's a perfect example of something the market CANNOT provide better.
In fact, health-care is logically the stupidest thing in the world to make subject to market forces. A sick person is by definition in-capable (or at least less-capable) of earning an income - and therefore less capable of paying for health-care. The only free-market answer is insurance - and since an insurance company is always incentivized to deny every claim and in healthcare you don't HAVE to be right - you just need to deny it LONG enough for the patient to die, that has made sure that a great many people who could have lived have been killed - people who HAD insurance, who paid their premiums, who got sick - and died from a curable disease because all of a sudden their insurance company just started making up excuses, safe in the knowledge that the stiffed customer won't live long enough to sue them.
As if that's not bad enough - you THEN also allowed them to deny service to people capable of paying based on ludicrous crap - so the only people who could GET insurance to begin with was those least likely to ever need it, so the insurance companies could run the ultimate protection-racket.
Just imagine for a moment living in a world where insurance companies was as scared of not paying a claim promptly as you are of missing a premium... that's the ONLY world where a free market healthcare system is NOT a disaster, and it exists ONLY in your imagination.