E.g. if someone _does_ try to create an NFT for the Mona Lisa, our ability to refute / accept its authenticity is premised on the knowledge that in the real world, the French Republic itself owns the work. How would we trust that the keys associated with minting the NFT were controlled by the French Republic? Presumably we'd need some public statement of attestation from an official French government body, and perhaps with the concurrence of others, to have confidence that this wasn't a rogue intern at the Ministry of Culture, or a hacker that got control to some official accounts or pages.
But applying this logic to "avatars" seems to be either broken or creepy. Who has the authority to say that you are or aren't you?