Your argument comes down to "but who's gonna build roads?" which is somewhat of a statist meme among libertarians. In short, it's this: roads are built by private contractors hired by the government, those contractors are paid by taxpayers money. Government acts as a middle man, which, indeed, may be necessary to coordinate the project, however it holds an ultimate monopoly for the middle man. There's no reason why one middle man should exist to coordinate building all roads.

When you talk about risks in undertaking an investment, it means there might not be enough demand for something that the government does and so taxpayers in fact are investing in things not enough people actually need to justify the investment. Which simply means that the government is an irresponsible fund manager.

A good way to get a free marketeer to stop talking is to ask them to come up with a free market system that doesn't end up hopelessly stratified. I don't know whether they shut down, like a killer AI given an unsolvable problem, or start reevaluating their views.