The problem is, I do not know of any doctors or other practitioners who care to work for free. Whine all you want about their desire to make a “profit” in exchange for their time, but I believe that, like all laborers they are free to work, but not likely to work for free — they deserve to be paid for their work. Since doctors, nurses, researchers, office workers and, yes, even hospital administrators demand a paycheck in return for a week’s work, medical care will never be free.
The question then is who will pay them. Either the patients themselves pay, usually through market-driven insurance programs, or tax payers pay, through government bureaucracies that are famously inefficient. There is no reason to believe that the government system would be cheaper.