There is basically no way to make progress here, as far as I can see. If the insurance companies weren't running open-loop before, they certainly are now.
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This option doesn't work because healthcare can't be a free market. Car insurance companies have to compete not only with each other but with alternatives like not owning a car at all. There is no alternative to being alive, so health insurance companies can effortlessly collude to raise prices across the industry knowing that they have the most captive customer base possible.