Regulation isn’t the reason those sectors aren’t free markets. On the contrary, regulation exists because they can’t be free markets. Both lead to market failures due to information disparities, principal-agent problems, massive externalities, and a lack of free choice (in the case of health care).
The issue is the amount of regulation, of course. Regulatory capture can have worse effects than most market failures, and healthcare is one of the most obviously "captured" sectors.
I would prefer more regulation to make sure prices are transparent. The current system is set up to make prices as opaque as possible. The employer has a lot of information, the provider has information, the insurance has information, but the patient is being kept in the dark. That is, until the big bill comes in the mail.
