... every other developed, relatively wealthy country has put together a better, less expensive system.
It's a shell game, $$-wise. Residents of those countries don't pay $$ to healthcare providers or insurance companies, BUT instead pay that $$ to the government in taxes.
As to "better", why do Canuckians go to the US and pay their own $$ for some healthcare tests and procedures? Why is "healthcare tourism" a thing in the UK? The answer is simple. Delays for tests, treatments, and surgical procedures are experienced by those countries' citizens as prolongation of pain and disabilities and sometimes even as preventable deaths.
