I'm actually not really. Here's at least a logical arguments one could make.

Healthcare is a scarce resource like all things. Making it universal doesn't exempt it from that fact. Removing it from a competitive market will likely make it more expensive and prevent innovations which will keep it affordable. Competitive markets drive efficiency.

Government provided healthcare rations service availability based on criteria they set. A private system rations availability based on the indivual's ability to afford the service. If people can afford the service additional capacity can be created with that money. Under a government system extremely long wait times are the norm .. With health this may mean late diagnosis of cancer and other suboptimal outcomes.

People are generally more wealthy in the later years of their lives and also in need of more care. Under a public system the costs associated with an aging population will be disproportionately placed on younger people who still pay taxes in their prime earning years. With the number of working people constantly decreasing when compared to the number of retired baby boomers this is unsustainable under a public system.

At the end of the day I think free markets apply poorly to healthcare because you have no ability to comparison shop during a medical emergency. Also US seems to have the worst mix of regulated private healthcare which has kept costs the highest of any country. I do think most social democratic countries are basically screwed over the next 20 years with the demographics being what they are.