Those roads and their economic merit predate the state's involvement. The might be lower quality in some places without the state subsidy but those roads would still exist.

See also: railroads

Here in the US, government is of the people, by the people, for the people. The municipal, state, and federal governments build and maintain public roads at and for our pleasure.

We haven't gotten into private and toll roads yet, either; the freedom for a landowner to decide what cars go where on his land.

So yes, cars in the US are exemplars of pure freedom one way or the other.