I don't know how to answer that. I think the system is pretty inefficient in a variety of ways. If you universalized Medicare, eliminating insurance entirely, you'd get costs somewhere in between Medicare's current admin overhead and the overhead of private insurance (you mechanically would not get Medicare's current overhead, because the majority of your customers would have much lower claims than Medicare's all-seniors patients do, and overhead is a ratio).
But the largest inefficiencies are all on the providers side. We simply pay practitioners too much, enforce artificial scarcity of practitioners, and prescribe too many services.
So if we're talking about "The American System" as a whole --- which is what the thread is about --- it behooves us first to consider the question "how much better would things be if we simply zeroed this category of expense out". The answer is, to a first approximation, we would get a 6.5% price break. I would not drive even a couple blocks out of my way to get a 6.5% price break on a pack of chicken breasts.
That's true, but it's a problem single-payer doesn't fix; that's my big issue with it (it locks in rapacious rates and preferences for the health provider industry, making them palatable to consumers by hiding the payer).
The complexity is far higher than credit card processing, including extensive price negotiation with individual health care providers. Though we call it "insurance" it's just as much a "buyer's club" for health care services.
Large employers (e.g. Google) are also generally "self-insured" meaning that the "insurance" component is offloaded to the purchaser, the employer of the insured individuals. In those cases, the health care insurer processes the claims from health care providers, determines if they were justified, or if the treatment/diagnostic/drug is justified by coverage determinations of the provider, etc, but the employer (e.g. Google) just pays the claims in the end too.
