(a) A motor carrier may operate, for the purpose of picking up or delivering mail, parcels, or packages, a vehicle bearing license plates issued under § 551.452 on a public highway that is not an interstate or a limited-access or controlled-access highway and that has a speed limit of not more than 35 miles per hour.
(b) The Department of Motor Vehicles may not require the registration of a vehicle operated under Subsection (a) unless the registration is required by other law.