You could generate a signature that proves that you have the private key associated with the address
You can run a piece of mathematics that not one person in a thousand would understand, but there is no way to show it off, like in a book case or hang it on a wall.
But given that most valuable art is sitting in deep storage in free ports, I am not sure it is a problem.
Does John Cleese post this address in a tweet, or how is it associated with him?
Yes, he has done so.