The argument for private industry was never that they would always charge lower prices per unit, but that they would produce things more efficiently--at a lower cost per unit. Of course public providers can charge lower prices. Their sales revenues aren't their only source of funds! So the mere fact that they charge lower prices doesn't necessarily indicate lower total cost, since the low prices may simply be a subsidy which is shorn up with tax dollars.

A case in point would be the Mamdani stores that are being launched in New York City. They'll be offering groceries at a steep discount. Socialist activists could then turn around and write headlines like "private-owned grocery stores charge x% more for groceries than public providers", but would that mean that public groceries have overall lower costs than private ones? Obviously not. It would be foolish to use price data to argue that the public model is somehow better than the private one. You would need to know whether the point-of-sale savings represent actual savings to the consumer, or whether the difference is being paid in some other way.

It doesn't do consumers any good to pay $50 less their utility bill if that $50 savings is made possible by charging an additional $60 in state and local taxes.