If we're doing cryptography, then why go through the blockchain at all then? I could sell the original private key I used to sign the picture to somebody, and they can prove their ownership all day long. I don't see the value add of a fancy database.
You can't sell a private key because you can't provably delete any potential remaining copies you might have. You could continue to sell the private key to others.
Artist still could sell the same artwork multiple times on a single or multiple exchanges. Or someone could steal their keys and sell the artwork multiple times.