A free market implies that a doctor should be charging as much as he can get for a procedure in order to maximise his profits. Standard econ 101 stuff. However, when someone is dying, they'd happily spend every penny they have even if it's just for simple cheap antibiotics. Therefore, you can't let the standard "the price is what people are willing to pay" economics take control. Healthcare cannot ever be a free market in a just, moral society.
That's not to mention the socio-economic aspect of the healthcare system. If people are dying simply because a procedure is being charged at its free market value, then the poorer end of your workforce will be decimated. And yet, the poorer end make up the vast majority of jobs! Socialised healthcare of some sort is absolutely essential to a well functioning society.
The obvious counter argument is that I could pay for my highly skilled, valuable workers to have private healthcare. The free market at work! But what about the people who don't work for me yet are essential to my business? How do I ensure the guys who build and maintain my roads survive that potentially dangerous job? How do I ensure that the guys who take my trash out are covered? These are all fairly low paying jobs where the downward wage pressure would push them into not being covered.
Yet these people are absolutely essential to my business running.
Then there's my customers. I try and sell to all walks of life, rich and poor. Where's my market if all the poor are dying due to not affording healthcare?
/rant over
There's just so many reasons why free market healthcare is bad. Socialised healthcare isn't just good morally, it's good for business too.