> And hospitals will still have admin as they still have to bill the government.

Missed responding to this piece before, but, sure: but, from the source I cited upthread, BIR costs imposed in the US big public programs (Medicare/Medicaid) is 2-5% of total cost, in the US private insurance system, it's 17% of cost. With single-payer admin will be nonzero, but it also won't be nearly 1/3 of total health expenditures, nearly half of which is related to billing and insurance.