So does it follow that if you relocate to another state you have to start all over again ?

If so this makes our system very straightforward and efficient. Cue amazed expression..

Yes! I'm in the process of buying an older Morgan in Ohio to take to Florida (my first Morgan) . Will need a new Title, plates, and registration. Will take multiple trip to the DMV most likely. The odometer is often challenged in this sort of scenario.

Unfortunately Australia is like that too. Transferring a vehicle from one state to another can be a nightmare, as some of our Oz TM members can testify. Licencing and vehicle registration should be a national thing.
At least in NSW the insurance and tax goes with the car when it is sold and the transfer of ownership can be sent by mail by either party, however, to be sure it happens, it is best for the seller to notify the authority. I would think anything to do with the seller retaining a vanity plate would have to be done before the vehicle is sold. In effect a buyer can turn up with cash, spend a few moments completing documents, get a receipt for the payment, and drive away.

Here in Italy, whilst administration is regional, all licencing and vehicle registration I applicable nationally. They have investigated vanity plates but at the moment they are not available in Italy. All plates are issued by the authority and it is not possible to have your own plates made. Older registration plates used to be coded for the Province: an old plate starting CO was issued in the Province of Como. All new EU plates are national.

When a car is sold a change of ownership must be done by an agency, even though the title is now only electronic, and you must present ID documents and personal tax number. This naturally involves some time, arrangement, and the inevitable fee. The vehicle tax goes with the car, whatever is left of the year paid to date. Whilst insurance is not for named drivers the new owner must arrange insurance.

If the change of ownership could be done by the seller and buyer online it would be much simpler but I think the Italian government wouldn't trust people to do it themselves.

I have learned that e.g. in California a new car will keep its plate a whole life as long it is in California. If it is sold second hand to another US state it will get a new plate from there. What if a car goes back to California later on. Can it use its first original California plate again? E.g. a nice 60s black plate, or has it to be a new one?

Good luck with that, quite a performance but worth it in the end.

You are lucky. It took them 5 and a half months to reinstate my Cat C1 licence. I certainly don't think that is well organised.

It even gets crazier with medical licenses (I am a physician) as each state has its own medical board and you have to have a license to do any practice in that state. I got my first license in Oregon as that is where I was a resident (I let that lapse). Then Oklahoma where I had my practice (still have that one). Then moved a few times after I got into Medical Education. So I currently have a Virginia license and have had (but lapsed) one in Pennsylvania and Texas.

Each board has a different set of rules for your application, an application fee and an annual or biannual license fee!

Unless, of course you work for the military, the VA or "Indian Health Service" in which case you work for the US government and "any state license" is all you need.