There is a great counterexample that is Kaiser. They are a private health insurance org that provides massive savings by simultaneously also running a network of hospitals and outpatient facilities. Notably they are not-for-profit. So that's perhaps what we're shooting for "all the goodwill of government, without the mucuousy bureaucratic slop in any government institution"
If only all the private sector orgs were Kaiser, not for profit and for the well being of humanity. Kaisers of the world are a flash in the pan, "don't be evil" googles only to become "be evil" googles.
I would simply recommend to look at how Singapore does things and copy that, after all, that's what China did and look how well they have done economically.