Errrm.... yes there is.
There are theoretical reasons: Economies of scale, for starters
No. As most Americans are already insured (and many who aren't are young, and hence don't represent as much per-capita load on the system), an increase to the entire population would not change the scale much at all.
as well as the reduction in paperwork / staff needed to do means testing
Where's the evidence that means testing represents a significant portion of our administrative costs?
claims reviews, claims refusals etc.
None of that would stop or even reduce with 100% coverage. You seem to be thinking about the administrative advantages of a single-payer system, but that's
different from the administrative advantages of everyone having insurance.
There are also empirical reasons: Countries with universal healthcare systems (even those where universal coverage provided by private enterprise) often spend less per capita in total than the US currently spends.
I keep hearing this, and the cost differential is quite real, but the numbers never add up to a case for America adopting UHC based on cost advantages. The idea that our costs would drop to the level of those other countries by expanding coverage just doesn't add up. Nobody can point me to any quantitative evidence of the savings we can realistically expect. There are inefficiencies in our system, but there is no indication that the inefficiencies are that large, or that they can be eliminated so easily.
The figures also suggest, if I remember correctly, that the % spend on overheads is much, much higher in the private compared to the pubic sector.
Enough to close the gap between us and other countries? No, I don't think so.
"the New England Journal of Medicine estimates that administrative costs take 31 cents out of every health care dollar in the U.S., compared to only 17 cents in Canada."
But cutting down our administrative costs to Canadian levels wouldn't bring about cost parity, not by a long shot. Hell, eliminating our administrative costs completely (which isn't possible) wouldn't accomplish that. Like I said, the numbers don't add up.
Americans do not demand the same things from our healthcare system that others demand. We demand access to the newest drugs (something many single-payer systems refuse outright to keep costs down), lots of high-tech diagnostics like MRI's, and expensive end-of-life care. You can argue that we are wrong to do so, that we don't get worthwhile care for the dollar, but the demand is there. And that demand won't go away under any universal health care system.