The analogy to fire departments doesn't work. Your fire insurance doesn't pay the fire department to save your house, it pays you to repair/replace it. That one's free market all the way.

Furthermore, there are many free markets in which consumers cannot be fully informed which work just fine. I know very little about the design of video cards, the maintainence of automobiles, how to remodel a house, what makes a good lawyer, whether my glasses are good for my vision, or myriad other things I pay others for on a regular basis. Nonetheless, I am able to navigate these markets just fine and make tradeoffs according to my personal values. The combined effect of consumer reports, public opinion, and paid personal advocates seems to get me there okay.

I submit that in a free market, most would have no more difficulty shopping for a docter than they do for a mechanic.

And while patients cannot choose when or how to fall ill, they can choose what to treat, what to treat well, what to invest in preventing, and what to simply tough out. The dire necessity of my owning a car does not prevent competition between car dealerships.