First of all, you're essentially talking about DRM. The signed and notarized contract is what determines ownership, not the NFT. It's centralized in (and can be modified by) the legal system.
For example, that contract could be nullified or invalidated by a court opinion, and the NFT becomes meaningless. It's just a digital document with a paper trail.
Think of it like this: does a Google Photo become more useful if A) it can only be on one computer at a time, and B) I have a log of every computer it's ever been on?
I could also copy the embedded digital asset and put it into a different NFT. Then there would be two NFTs with the exact same "proof" in them. Which is the real one? The document can't specify which NFT it applies to because the NFT is minted after the document is signed.