But you can't prove ownership of the actual art, with an NFT.

You can only prove ownership of that specific crypto transaction, which might be just a fake NFT, or duplicate.

There is nothing about crypto that actually proves it was the "real" NFT, or real art.

You need something else to actually prove that you own the "real" piece of art or NFT.

> Not identifying creators

If you are unable to identify creators then you are unable to prove ownership, because that NFT could just be a fake one, or even a duplicate that the creator has issued many times without you knowing it.

With crypto alone, you'd only be able to prove that you own something that might just be a fake or duplicate, and anyone can make as many fakes or duplicates as they want, so that's not really proving ownership.

You are conflating several issues. Yes, a creator presumably would have ways to cheat the system, for example by selling the same thing on different blockchains (as mentioned elsewhere). But eventually they would be revealed to be frauds and presumably the worth of their creations would plummet.

To verify the identity of a creator is a solvable problem, though, and is also yet another issue than the "sell it multiple times" problem.