A centralized company running a database absolutely can provide digital scarcity. If they could not, then why would there be a real money market around in-game items for many games (which may include some limited run or even one-of-a-kind items).

Sure one can say that NFTs are uniquly identifyable. But that does not mean very much. People might claim it means the owner of the database cannot just make your unique item into something super common by creating many copies.

But they still can create many nearly identical copies differing basically only the NFT token's id, which in effect would act like a serial number.

I don't see this providing any scarcity that a centralized list of "offical" owners does not provide.