Its a very complicated system yes.
It is not a free market but it operates with little government oversight.
It operates with collusion. ITs not quite a monopoly and there are numerous healthcare providers, but there is collusion between Insurance and hospitals and physicians and pharma to increase revenues for all 3. They double or triple healthcare costs.
Government intervention in healthcare would DRASTICALLY reduce costs, even with the inefficiency of government programs. Only problem would be salaries of the top 5%.