I don't think you understand what the word efficient means because what you said about it is certainly untrue. The private sector will almost always deliver a better result as long as you mitigate market power abuse. You are basically saying it is more efficient to deliver services through a public system because said public system failed at mitigating market power. In the rent example a lot of that market power is even self inflicted by said public sector via onerous zoning and permitting regulations that make development only plausible via large, oligopolistic systems.