Got it a little mixed there, John. I assumed money going back to the Fed was 27¢ admin cost. The $1 figure would be money spent for other necessities, like clothes, TP, dish soap, etc.
As for the money going back to then fed, and then States, the reason is, to me, obvious: too many states wouldn't offer the programs. America saw this when Social Security was in the process. When FDR signed it into law, only 17 States had any old age pension program. A lot of lobbying was done by the FOE (Fraternal Order of Eagles. Member in good standing Aerie 395)
and since FDR had been a member for years, he was happy to sign it. But only 17 States had any such plan. Thirty-one did not!
Obamacare has its critics, but will lead the way to single parer eventually. But the conservative States continue to fight it. This is why the federal government has to oversee it. They set the minimum standards, and it is up to the States to determine to add to it.
Sorry it's so long, but I'd sound like a jackass if I just said "it's obvious to me".