Given the fact the constitution limits the govt and not the people.
Given the fact the constitution says the govt cannot limit the freedom of movement.
The govt cannot make laws limiting freedom of movement regardless of the method as they were not given that right by the constitution. Therefore driving as a form of movement cannot be regulated.
There are also precedents discussing it
Thompson v.Smith, 154 SE 579, 11 American Jurisprudence, Constitutional Law, section 329, page 1135 “The right of the Citizen to travel upon the public highways and to transport his property thereon, in the ordinary course of life and business, is a common right which he has under the right to enjoy life and liberty, to acquire and possess property, and to pursue happiness and safety. It includes the right, in so doing, to use the ordinary and usual conveyances of the day, and under the existing modes of travel, includes the right to drive a horse drawn carriage or wagon thereon or to operate an automobile thereon, for the usual and ordinary purpose of life and business.” –