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Pardon me?

Surely your concepts of a "free market health care system" and one "that is not written by insurance companies" are flatly contradictory? 

The very essence of free market insurance (health care or otherwise) is that competing companies get to compete by devising different policies and different rates ("written by insurance companies") designed to appeal competitively to consumers. In this, free market insurance is like any other consumer product. A significant difference from other  consumer products is that in free market insurance companies also get to compete by selectively refusing customers on the bases of current or projected future health.

The moment one allows government to intrude into the freedom of insurance companies (1) to write their own policies as they bloody well want and (2) accept/reject whomever the bloody well want as customers, you have left capitalist insurance and moved towards socialism. This is not a dichotomy, but rather a continuum.