There are no purely privatized (or capitalist) systems, because this is impossible.
All the roads and streets being for-profit and privately owned, for example. Sections of a river and thye water in it being privately owned, for example.
There are also entirely no purely collectivized societies.
Even in North Korea, people own their own clothing, furniture, toothbrushes and such.
Each and every human society is partly collectivized and partly private.
So we cannot exclude all privacy or all collectivization. When we discuss political systems, we are talking about the mix.
I say we would be better off with collectivized health care, because free market economics and competition cannot work in health care.
You cannot compare prices of open heart surgery at Hospital A with that of Hospital B after you have had a cardiac infarction.
Most hospitals refuse to even tell patients what their procedures cost prior to performing them. They prefer to force thew hapless patient to sign an agreement that is essentially a blank check, obliging this to pay whatever the hospital business office can dream up.
This is where government must step in and tell the hospital that they MUST provide a set fee for specific procedures. Mechanics must do this, contractors must do this.
Every advanced country on this planet has some form of universal health care. Obama was victorious in getting this started and there will be no going back.
Three cheers for President Barack Obama! Hip hip HOORAY! Hip hip HOORAY! Hip hip HOORAY!