For any other use the situation is more complicated. Some NFTs confer ownership and/or use rights.

There's additional value with FNFTF in that users who are thinking of purchasing an NFT can have confidence they're not buying a copy that may not have the value, confer the rights, or provide some additional benefit they think it might.

Like any other counterfeit good, as we speak someone is buying an NFT as (if nothing else) an asset class and paying what they think it is worth. If someone is spending tens or hundreds of thousands of dollars on an Ape (for example) they may find out down the line that it's a copy and no one considers it to be worth anything. This isn't an different from forged works that have been sold for all of human history.

Then there are marketplaces and other uses. Marketplaces can use the underlying API powering FNFTF to prevent copied content from ending up on their platform, removal of fraudulent/inauthentic content, etc.