This objection is often made about anarchism, and more generally libertarianism. However, except perhaps for national defense, libertarians can quite easily come up with historical examples of service X being provided without State intervention or aid.
Private roads were built by colonial Americans, for example. And even governments today generally hire private builders, albeit with stolen money. "But who will build the roads?" is a standard joke meme among anarchists. It's like a pro-slavery person asking "But who will pick the cotton?"