The Federal Constitution also requires that a State have a "republican form of government." That means the rule of law, and a Constitution that enumerates the limited powers of the State. If a State's Constitution does not grant it the power to regulate or criminalize vehicular operation or travel on roads, then any such laws or regulations are unconstitutional. Note, however, that a Constitutional grant of a general power to make laws and regulations to secure public safety would suffice.
Right. And that blanket rationalization for any public law would also allow for video's installed in your home.