Given the heavy involvement of the state in funding and directing care and research, I don't think anyone would describe healthcare and medical research as a free market.
Yeah but that's more because of lobbying and politics than logical, economic approaches to problems. It's not like when I go to the doctor everyone's incentives are aligned. The insurance company is still actively working against me, just now it's really complicated how they do it due to regulation so only they can play the game and I just have to take their decision until it's worth getting lawyers involved.