Our UK road tax used to be the paper disc that had to be displayed in the tax disc holder (motorcycle) or lower left-hand side of the windscreen (car etc.), however, it's all computerised now so there's no paper disc anymore or anything else that has to be displayed, stuck on or carried as the police/authorities can tell if a vehicle is taxed, insured, Mot'd and who the 'registered keeper' is from the registration mark.
With the UK system, the 'plate' (registration mark) normally stays with the vehicle unless it's one of the personalised registrations.
In the UK the taxation class of the vehicle isn't anything to with ownership.
Same in the UK now which requires a trip to the post office who check documents and send the old V5C registration document to the DVLA (Swansea) who then issue a new amended V5C to the named 'registered keeper' as the DVLA isn't concerned with ownership only who is legally responsible for the vehicle.
https://www.askthe.police.uk/content/Q743.htm
UK historic tax is free but it still has to be renewed annually which I agree is unnecessary bureaucracy but it only takes a couple of minutes to renew online!
There's no MoT (annual inspection) required on historic vehicles now so it's one level of bureaucracy that's been removed.