Think about the market's provision of grocery stores: plenty of competition. Most places they don't enjoy geographic monopolies like car dealerships do. They manage to get one of the most vital goods to a huge population spread across a huge area on time and at a great price, with local variations anticipating the specific desires of local consumers. There is no central coordinator or Department of Grocery Services. The market figures it out.
How can someone look at healthcare, with its absolutely absurd outcomes, and not understand that it is precisely because of government interference that nothing makes any sense? Costs keep rising unsustainably, which is the opposite of the way markets work. Paperwork and administrative staff balloons in proportion to patient care.
Once the state gets involved, now it becomes political. Do you think the current political climate in the US should be further embedded into healthcare? If the state controlled everything, then you'd get outcomes like red/blue states losing/gaining funding depending on the results of the most recent election. One could imagine more dystopian outcomes quite easily.