Generally, no I don't. I have basically two hospital systems to choose from. All specialists I require seeing are only available in these two hospital systems if I want to be covered by my insurance. I can see a variety of primary care physicians, but I cannot see e.g. a rheumatologist outside specific hospital conglomerates.
But insurance networks aren't a requirement of free markets. So your argument that in today's system (only one form of a free market for healthcare) proves free markets don't work is ignoring alternatives.
It sounds like you actually would have plenty of physicians to choose from, just like when you buy food.
