> ...bureaucratic overhead extracts a few more percent.

Respectfully, my perception contradicts this. My GF has been a psychologist for 25 years. For the first half of her career, funding for her work was provided exclusively by a state program (California), but about 10 years ago, the funding transitioned mostly to private health insurance. And it's been a bureaucratic nightmare every since. She had to hire a skilled/well-paid FTE just to manage the billing with the private health insurance companies. And it's still a nightmare to deal with. So yeah, to downplay the "bureaucratic overhead" of private insurance, is not universally accurate, IMHO. Maybe for big hospitals, it represents a small percentage of overheard, but not for smaller providers.