With multiple “single-payer” systems in the same population (often serving overlapping populations with each other and private health insurance) you've negated that benefit.

You’ve also negated the market power advantage of monopsony purchasing by having multiple of them, and again having them coexist with private health insurance.

(And that's even before considering that while Medicare and some state Medicaid plans have single payer components, Medicare is not a single-payer plan covering the listed number of beneficiaries, but instead just under half are in the single-payer traditional Medicare, and that Medicaid isn't a single payer plan, or even a plan, at all, its a funding mechanism for state-operated plans, each of which may or may not operate entirely as a state-level single-payer plan.)