But a ledger doesn’t prevent copies of the art or duplicate tokens it just enforces uniqueness of the singular token. So you’re still left with the uniqueness problem. Essentially trying to create scarcity where there is none is a spectacularly silly idea.
1. I am artist X
2. I have an Ethereum wallet and even own the ENS name X.eth
3. I mint an NFT that represents ownership of one of my digital works
That NFT cannot be duplicated, because the Ethereum network enforces unique IDs for each ERC 721 token and prevents the double spend problem. What's more, I can look at the NFT and determined that it was indeed minted by artist X because it was his address that created it.
The artist can later mint duplicate NFTs but everyone will still know which NFT came first.