The biggest barrier to the operation of the free market in medicine is the medical licence, especially as being a legal and economic barrier to prescribing drugs, ordering tests or referrals to the actual specialist who can help you
Most prescription drugs have significant risks and side effects. Or in the case of antibiotics, overuse leads to resistant bacteria. That's why they're controlled instead of being sold over the counter. Some states do allow allied health practitioners such as physician assistants and nurse practitioners to prescribe certain drugs.
You can order most lab tests yourself. Those might not be covered by your health plan.
Primary care physicians can do a lot to help you. Jumping straight to a specialist is usually a waste of limited resources. But some types of health plans such as a PPO don't necessarily require a referral in order to pay for a specialist claim.
If a free market requires unlicensed medicine, then no thanks! There are reasonable arguments for removing licensure from some other professions, but medicine isn't one of those. I'd argue that the US is actually too lax, allowing too many entities to practice medicine without adhering to professional standards.
