Okay. Let me think on this a bit.
First, I think that a properly free market medical system would be the cheapest and most responsive. However, what we have is NOT a free market system, but a careful mix of the worst aspects of free market and government provisioning and regulation.
Consider the typical person, covered by a healthcare program(it's not really insurance) provided by their work. Said person goes to see a doctor in a clinic for a procedure. Doesn't really matter what.
Who's the clinic's customer? Believe it or not, it's not the person. It's the health insurance company that's paying them, has the pre-existing contract, etc... Who's the customer that the health insurance company is trying to please? It's not the individual - it's the business employing the individual. Thus, you're likely to get premium care if you're the CEO in charge of selecting the insurance company, but below that? Nope.
But in any case, the insurance company doesn't want to pay money - so you get copays, deductibles, and all that. Plus, they hire people to fight claims, rejecting them at the slightest excuse that won't get them sued. In order to actually get money, the providers have to hire people to submit claims. Now, competition has forced auto insurers to be efficient, but consider how many auto body shops there are compared to hospitals, and how many auto insurance companies there are compared to medical insurance companies. And you probably visit a auto body shop less often than a medical provider.
Now, this is even before you add lawsuits and defensive medicine. there's no competition, there's no up front billing, there's very little of anything. You get better, cheaper, results in the clinics that have the most economic freedom - Optical, dental, etc... Surgeons who do breast implants and tummy tucks and such can get their prices very affordable.
Anyways, consider a single payer system - There's only one 'company' to fight with, and in many cases they at least realize that they're going to pay out what they're paying out. There's a lot less paperwork expense, and they aren't charging by the nitnoid expense like giving somebody a Tylenol in a hospital.
What really gets me is that the federal government spends enough on healthcare that, if we were paying what Germany, Canada, and France were, we could provide universal single payer healthcare for not one additional dollar. Add in what the states pay, and we'd have quite the surplus, or be able to pay more per individual.