The application becomes the central authority for some arbitrary token. Yes, in theory they could use "an NFT" to represent a key to some in-application capability but at best the owner of the NFT has an exclusive right to that capability at the whim of the application owner. The NFT owner can't really claim to own any real "thing" in and of it's own right.
The application owner gains very little – they could just implement a Plan Old Database within their system.
The owner of the "NFT" gains very little – except the theoretical value of a token they could trade, and might have value, as long as it's backed with some capability provided by the application.
None of this applies to things like "a gif on the internet", for which the NFT means exactly nothing if you have no enforceable rights.