If people weren't stupid they would not put up with having the highest medical costs in the world while achieving the lowest quality of care in the first world. Health Insurance Companies exist because too many people haven't figured out that their purpose is to limit, or prevent, actual health care.
Mmmm the existence of these companies is not enough to say people are stupid. Plenty of places have these companies and reasonable access to high quality care at a reasonable price. It's just the US in particular allows their companies to get away with murder.
Even with universal healthcare, someone has to do all the admin stuff, and putting it under government control directly just screams of inefficiencies.
I always assume people who assert that the government is automatically less efficient, more expensive, and poorly run compared to private industry must never have been associated with a large corporation, or lack awareness.
Medicare, as it exists today, delivers superior care at lower cost than any private insurer. This despite the fact that Medicare covers the elderly and disabled, groups that need more care than the population at large that the private guys cover. If you think about it, Medicare is a giant subsidy to the private market by removing needy populations from their rolls.
The scheme to include private guys in medicare "medicare advantage", was supposed to bring down costs by bringing in the efficiency of the private market. Medicare Advantage today costs more than the Army and the Navy.