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Nothing, but they can only sign the "first" once

They could mint or 'sign' as many as they want.

But like a painting that can be copied, people decide to disproportionately value the first one...just because.

sure, but unless they are signed in the same block, then there will be a "first".

If the NFT is just a pointer to a digital good, can't they have multiple "first" NFTs all referring to the same digital good?

Yes and no. If they minted multiple within the same block then yes. If not, then proof of first minted NFT could be verified by block height.