There is not any federal law preventing moving a mobile home (making it thereby an “immobile home”).
The concern is that pre HUD (before June 1976) homes were not inspected according to a standard code, including construction safety requirements. As a result many movers will not touch a home without a HUD plate on it. For the ones that will consider it won’t offer any assurance of their services, or insurance if something does go wrong.
Local and state laws prevail - for now.