Sorry, but we have the MOST free market in the developed world when it comes to healthcare and it drives costs up. The free market is great for some things, but it's not the panacea that people think it is.
Also, you say "We have a legally entrenched doctors guild with a government granted monopoly on their profession" So are you saying that we would all be better off if anyone who wanted could call themselves a medical doctor? And if that is not what you advocate, then what is your specific plan?