There are plenty of things that government does poorly. Or, at least you can make that argument, and find some support for it out there. For instance, many people believe that government does a terrible job at sparking innovation. I could imagine a debate there. Some think that government does a bad job at providing choice. That’s entirely defensible. Government run systems also allow less room for profit, which can drive out entrepreneurs. Also arguable.
But what government systems do well is hold down costs. They use central planning. They use their large market power to negotiate for reduced reimbursement (see Part 2). They buy drugs cheaper. They eliminate profit and overhead.In a lot of ways this still understates the role of government in health care. The regulatory rules about health care are aslo responsible for increasing prices as well and have some definite effects on innovation. Now I happen to think that some of the rules are good (e.g. the FDA) and some of these rules are bonkers (e.g. limits on number of new physicians via residency slots). But there is a point where you have to decide how you want a market to be run. Designing it so that it regulates things that help interest groups (i.e. keeping physician numbers down) but not other things (i.e. reducing costs by using market power) is very much the definition of regulatory capture.
I am quite willing to have a discussion about free market health care. The first barrier to a real free market system is how we deal with public health. After all, it took government intervention to get sewers and outhouses to come into common use in Europe. Just look at the complexity of the modern sanitation system in France. There is a conflict between the freedom to dump waste on the streets and the need to protect the public from fecal borne disease. Similar arguments can be made with the need to try and keep antibiotics effective.
A system that keeps all of the regulatory barriers to entry but shifts costs to the consumer is a very partial form of opening an industry to the free market.