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.
Many different applications can build on top of this open authenticity verification. This decentralised layer for authenticity verification is much more powerful than a single application builder can achieve with their own database. The concept itself is very powerful for interoperability but some of the valuations of assets currently feel ludicrous.
But authenticity of what exactly?
If everyone agrees that, for example, a particular distributed ledger provides authenticity of some class of artwork, that is fine. But soon the real world happens eg. a court in one country orders the art to be seized and handed over to a third party , but they don't have the ability to force the NFT to be transferred because the former-owner is in a different country. Would the art world suddenly pretend that the artwork is not real because the current owner does not have the NFT? We are back to square one.
And on top of all that, assets from one application can be integrated into another application. If I build a game and I allow people to use the "sword of NFT" they have from another game in my game then I've created a big incentive for people who like that other game to also play mine.
Meanwhile there is very little incentive for some other application to use those same tokens when their value is contingent on the whims of the original issuer. You're tightly coupling your business and liability to some other party who hasn't made any guarantees, promises or agreements to you. Its a can of legal problems.
Ultimately is like trading Apple gift cards, Pre-loaded debit cards, phone cards etc - its an abstraction in which then value of the token will only ever be less than the cash paid for it up-front, and most people trading them have some other reason for taking the hit (ie money laundering, fraud, etc)