Everything indicates that if you apply for this USDOT registration, you are impersonating a US employee. I can see something in the idea that an original right to travel, should it exist at all would be for all America so you might have the interstate aspect to it. But it sounds as if while you may be successful at having USDOT markers instead of license plates on your private vehicle, that you are getting the privilege of insurance which is only for government employees to enjoy. It sounds very dangerous to impersonate a government employee to get free insurance coverage, especially after an accident where you need to file a claim.