A Single-Payer-System would also be cheaper in the US. Nobody expenses as much on administrative cost, nobody pays so much as a % of GDP on Healthcare as you, still you have the worst health outcomes of all developed nations.

Taking into account both the costs of coverage expansion and the savings that would be achieved through the Medicare for All Act, we calculate that a single-payer, universal health-care system is likely to lead to a 13% savings in national health-care expenditure, equivalent to more than US$450 billion annually (based on the value of the US$ in 2017). The entire system could be funded with less financial outlay than is incurred by employers and households

https://www.thelancet.com/journals/lancet/article/PIIS0140-6...

Looks like I don't have access to the full paper, but I would be extremely skeptical of any claims with such accuracy or certainty.

The healthcare industry in the US is massive and already full of corruption and inefficiency. Even if we are to assume giving politicians and bureaucracy more control over the system will reduce both issues, we can't predict how successful that will be.

Similar claims were made regarding the hopes for ACA reducing costs and here we are.

You are, of course, aware that the current US single payer system (Medicare) subcontracts their administration to private health insurance companies? And that the "overhead" typically discussed when talking about Medicare doesn't include said companies but is instead only the overhead of what it takes to shovel money from the IRS to private insurance companies?

No, this is not Medicare Advantage, in which Medicare just directly pays private health insurance premiums for enrollees.