Why don't conservatives push for an actual free market when it comes to healthcare?

I get why people have reservations about a government run healthcare system. While it provides universal coverage, it comes with a ton of problems as can be observed in many countries (Canada, UK, etc.). Conservatives often counter that idea with saying the free market should control (which I tend to agree with). But the current system we have is anything but a free market. Buying health insurance as an individual is extremely expensive. Most affordable plans are obtained through employers or unions. Those organizations usually contract with a single provider, offering the member no actual choice. The more affordable plans drastically restrict which doctor's you can see and what services are available. There is very little choice. On top of that, there is very little price transparency. Hospitals overcharge for everything (e.g., the $100 band-aid), and often will not tell you how much a procedure costs until you are charged. Consumers have no sway against health insurance companies cause they're small fish. Only large organizations who buy group insurance plans do.

So why don't conservatives push for an actual free market? Divorce health insurance from unions/employers and create an actual free market for the whole country?