This is an excellent point, but it needs some further comment to explain why "contract law" doesn't necessarily apply well in the case of medical insurance.
As per your description, a medical insurance policy is a "contract" between an insurer and an insuree that provides for terms of payment for some other largely unspecified "contract" between the insuree and one or more medical professionals. In other words, there is already a third party in the U.S. health care system: the insurer.
Having this "third party" system in place -- regardless of whether the third party is a private insurer or a government agency -- is what makes our entire health care system fatally flawed. An economic transaction where a buyer (a patient) and a seller (a medical professional) conduct business between themselves while a third party ends up paying the bills is doomed to fail. And it has.
BINGO !!!!!