The major problem with the American healthcare system is that it has no prices, making it a completely non market system. It also has a massive redistribution from whites to nonwhites, which wealth redistribution system disrupts the provision of healthcare. What tends to happen is a hospital treats a hundred illegal immigrants for morbid obesity, and they do not pay their bills, and then it treats one white male, and he does pay his bill – which is set high enough so that the one person who pays covers the hundred people who do not pay.
The best system is Singapore, which has a socialist healthcare system for the poor, and the most Ayn Randian hard core capitalist healthcare system in the world for everyone else. Which system provides healthcare at a fraction of the cost of everyone else’s system and for the most part healthcare of substantially better quality.
If you are poor and sick, or sufficiently healthy that the quality of your healthcare does not matter much to you, you go to a government owned hospital, consult with a government employed doctor, buy government owned medicines from a government owned pharmacy. Otherwise, you just pay for it as if you were hiring a plumber to make modifications to your bathroom. The major government intervention in the private sector is making pricing information accurate and available. Private healthcare practitioners are free to dump people who will not or cannot pay on the socialist sector, or just not let them through the front door if they fail a credit check.
So the explicitly socialist system takes care of the pity cases, and the explicitly capitalist system takes care of everyone else. So everyone else gets the benefits of capitalism, and only the poor or the healthy suffer the consequences of socialism.