"Insurance administrative costs
in the U.S. are a significant portion of total healthcare spending, typically ranging from 15% to 30%, with some estimates putting total administrative burden even higher, at one-quarter to one-third of all healthcare dollars, primarily due to complex billing, coding, and insurance processes. While public programs like Medicare have low overhead (2-5%), private insurance and hospital systems face much higher administrative loads, significantly driving up overall U.S. healthcare costs compared to other countries."

Maybe I'm asking the question wrong.

You are, I think.

The federal government publishes a host of data about National Health Expenditures at the link at the bottom of this post, and Table 4 breaks down cost by program and expense. We see that the net cost of private insurance - basically the administrative load of all private health insurance - is about $150 billion. That's about 11% of total private health insurance costs...but it's only 3% of total national health care spending. When you look at the possible delta between the private load and the Medicare load (going from 11% to 3%), you're only at about 2.4%.

Again, a rounding error.

The reason for the discrepancy between those figures and the ones you cite above is that these are the costs on the insurance side, while the higher 15-30% estimates are based on some estimate of measuring provider administrative costs. But it's not kosher to add those back into the equation for private insurance and not for Medicare for all. Why? Because Medicare also has lots of administrative costs and recordkeeping requirements. In fact, since more medical care is already being provided through Medicare and Medicaid ($1.9 billion vs. $1.5 billion in private insurance), if the U.S. system has massive amounts of administrative load on providers it's a pretty good indication that the public systems are also putting providers through the wringer. Switching to Medicare doesn't make administrative load go away. You still have to keep medical records, still have to code and bill and follow up with recalcitrant payors, handle records requests from patients and deal with all of the hassles that come from providing medicine in the American system.

Which means there's not going to be much savings with a switch to single payer. Virtually none on the insurer side, and very little on the provider side. Which, again, is why state efforts to do this have all come to naught.

cms.gov - Nhe tables