I don't know for sure but the UK must be unique in the world that people are able to have their own plates made. Everywhere else you have to carry the government issued plates. In that case usually classic plates stay with the car but if they are replaced for any reason they are replaced with modern plates. Some places will reissue classic plates as personalised plates, but even that is rare.
Americans certainly can have " vanity" plates and I am sure it's possible elsewhere. . Why not? I watched an auction recently when one plate sold for 75 k euro and many were above 10 k. I'd like to think that it reduced my tax bill but somehow I doubt it.