Monopolies are bad for consumers. Single payer would be a giant monopoly with no competition to ensure quality and value.
You have theory. I have reality. Most of the advanced world has a single-payer system, and their health-care consumers are far better off than Americans. When theory contradicts reality, it's always the theory that's wrong, not the reality.
A
for-profit monopoly would be bad for consumers, by the way. But we can't treat health care as a free market, because it isn't one and never can be one. You can only have a free market when consumers are free not to buy -- and I don't mean not to buy from any one provider, I mean not to buy from ANY provider whatsoever -- and when merchants are free not to sell.
There's the flaw in your theory, and the reason why it does not comport with reality.