One key problem appears as misaligned ("perverse") incentives. But it has to be that because its essentially impossible for an average person to purchase health care in the moderately informed and choice-filled fashion that I can purchase a vacuum cleaner.
Of course, another key problem is trying to divide distinct parts of health care into distinct costs. Everyone benefits from having a good quality hospital in their area and so assigning a health care provider's cost to just a given patient and then trying to reduce the patient's cost is quite irrational.
Essentially, you have a public good that the state and private interests are trying to make into a public good. A lot of profit comes from this but little good for the patients.