I am not sure what you mean by this. Are you referring to art being duplicated, or a digital signature? You can verify that its a forgery, or from a different account than the first author. The digital signature isnt something you can replicate. You can print another one, but you cant duplicate the property of "first" itself.
I'm just as good as the most accomplished artist at reading numbers from /dev/random, that's why I don't see why one random-looking string would be more valuable than the other.
That depends on who thought of making the NFT first. Which isn't necessarily the artist.
> or its proven to have been generated by a person who exclusively had a certain private key
That has the same problem, it's generated by arbitrary pseudo-random numbers, rather than a real, living human hand. Look, I'm not disputing the underlying cryptographic principles. I'm happy they exist, because they are immensely useful for many purposes, like securing communication and financial transactions. I just struggle to see the artistic merit in someone having pulled some numbers out of /dev/random and having done some math on them.
The authenticity of this is easily verified by querying the transaction directly from the on-chain smart contract.
There are other blockchain/crypto art projects that use the chain itself to store data; such as Autoglyphs[2], which is essentially a first of its kind generative artwork on Ethereum coded entirely within the Solidity smart contract. In this case there is no question about the authenticity; you simply look at that contract address and the tokens it initiated.
[1] - https://hicetnunc.xyz/