The primary advantage is increased trust. With a SQL database, it is necessary to trust the organization that hosts the database. With blockchain it is necessary to trust a distributed network of organizations (or more precisely their computational power).
If you think that NFT issuers are more trustworthy than banks or big companies then I have bad news for you. The NFT you get is as trustworthy as the paper you bought saying you own the golden gate bridge. Nobody can take that paper from you, but they sure can take the bridge.
The question was (paraphrased) "what value does blockchain add over SQL database table with a unique index?" - not whether NFT issuers are more trustworthy than trusted organizations or if NFTs are a valid asset class.
But it isn't the same, with NFT's the trust comes from the NFT issuer and not the blockchain. With bitcoin you just have to trust the chain, but with NFT's you have to both trust the chain and the issuer.
I think this is a misevaluation of the trust involved. NFT's are using the blockchain to whitewash trust, the blockchain contains a smart contract and a URL. It provides no assurance that the URL contains the same contents as when the NFT was first minted.
With how most NFTs are implemented you need to have trust in the blockchain it self, in the implementation of the smart contract, in the server hosting the referenced metadata URL, and the server hosting the actual digital asset the NFT represents. If trust in any one of these is misplaced it can undermine the trust placed in the others.
The blockchain can not provide more trust than the least trustworthy part of the rest of the NFT chain. Since the URL referenced in the blockchain is likely stored in some single organization's SQL database, the maximum trustworthiness of an NFT is never going to be larger than the trustworthiness of that SQL database.