Sure, and universal health care helps even more but it doesn't fill the pockets of the members of the medical associations the way private health care does. Regulatory capture in its rawest form.
I disagree with private healthcare but there are ways to make it work.
Here is the basic idea. People are sick and there are not enough doctors and not enough drugs. Cost of healthcare rises until more doctors can be hired. Thus there will always be enough doctors. It also rewards superior care by making superior care more profitable.
However, if you artificially restrict the number of doctors then you are going against the idea of privatized health care. Similarly, if its possible to buy an existing drug to monopolize it and raise prices you are going against the idea of privatized healthcare.
It's the same with student loans. You privatize education and make students pay for it. Fine. However, by guaranteeing loans you did the exact opposite. You simultaneously privatized it and nationalized it in a highly inefficient way.
What is stopping people from getting together and forming their own "universal health care" group? There must be millions who are in favor of it? Get 100 million people together, and offer health care to each other. What's stopping you?
Some of them would have to put a lot of money at risk. When they do that, they usually want something in return. Well this is how corporations were invented. And those are regulated.
Typically the State medical device licensing boards will stop you. Try this: get 1000 families to chip in for an MRI and techs to run it for the benefit of the 1000 and their families. When you apply for State permit to turn it on, that board will look at competition in the area and not allow it. The rules don't allow too much competition to drive down prices, so only the mega-corps typically can play the game.