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It fundamentally comes to that you can never fairly assume that the consumer of medical services or purchaser of medical insurance is a well informed consumer, so a "free market" assumption is always going to be a poor starting point to assume. Most of us, as pilots, are used to complex systems and needing to understand lots of fine print. That isn't how the average Joe or Jane lives their lives.
My other personal pet-peeve with our current system is that there are huge administrative and time costs that are not captured by any of the normal metrics. I'm referring to: 1) the vast resources private companies and governments have to pour into administering health plans for their employees; and 2) the huge amount of time both the insured and uninsured need to spend to pay medical bills and sort through explanation-of-benefits to ensure they aren't getting screwed over by the provider or their insurance company. Virtually all of this goes away under a single-payer system (unless an employer chooses to offer a supplemental plan, as would likely be allowed). Will there still be battles over coverage with a government-paid system? Of course, but this happens regularly with private insurance now, and an "independent" ombudsman program could help to address that concern.