[mbesto]

You just conflated two partners in the whole mix of what we call "healthcare" in the US.

Payers = Medicare for All, UNH, Aetna, etc.

Providers = Hospitals, doctors, medical supplies, etc.

It's entirely possible to have one payer and then having a governing body regulate a free market[0] comprised of providers in the market.

[0] - I'm using the word free market not in its purest form (which rarely exists) but rather in a more colloquially way.