It shows how the art has changed hands and been transacted over time. That is an incredibly difficult thing to do in the physical world over hundreds or thousands of years.

You are correct that at the very initial point of minting there still needs to be some proof (i.e. artist cryptographically signing the data of their work with their private key), which as I understand, is not something that's really done currently (and should be).

Right but an NFT is just a link to a URL so there is no guarantee that it points to what it did originally or points to anything at all. All it guarantees is the provenance of the token, not the art itself.

Yikes. OK that seems like not a proper use of all this, then!! Seems like it would be more valuable to transact with just the artwork data signed by the artist's private key maybe with a bit of other metadata. But a URL??? Sounds like a lot can go wrong with that.