NFTs only solve one part of the problem though - rights management. You still need a good way for a cosmetic designed for game X to work in game Y. That's similar to any multi-platform development challenge. There are many other economic decisions that will have to be experimented with, including tax collection, platform fees, creator fees on resale, etc. It needs to work for everyone or it won't get the reach it needs to really empower users.
Whether or not NFT actually add anything here comes down to the remaining technical challenge of interoperability. Is it common for parties to agree on a common asset definition but not a common rights management platform? That's the situation where NFT help.
edit: To clarify, I'm not talking about regular NFTs as currently added by game developers where they're basically just a ticket to an ID referencing something created by the game developers and hosted on the game servers. I'm talking about trying to create a system for NFTs shared between games from different developers.
There is a huge market for content creators having large fan bases that literally pay them money via subscriptions, merch, etc. while they broadcast their gaming sessions live online. The entire business model for Epic's Fortnite is all cosmetic items via season passes, in-game transactions, etc. The game is free to play.
If content creators were to issue NFT's that represented a cosmetic item badge/emblem, which could be bought/sold/traded on an independent marketplace and each game studio was pressured to allow these emblems/badges across games then the content creator would profit on transactions and possibly the game studios could profit - maybe they get a cut via smart contracts if that's possible.
It wasn't very long ago that cross-platform play was not allowed by Sony and Microsoft and the game studios and players pushed for it. Major games have cross-platform play now, its expected in multi-player console games. Cross-game cosmetic items could be a huge thing for studios, indie content creators and and an opportunity for always online game platforms to get income from marketing/advertising. When there's a new comic book hero movie coming out, the movie studio could release cross-game cosmetic items (i.e. look like spidey) that players could then sell/trade later on. I would agree you don't need the tech from crypto or NFT's to accomplish this but it sounds like that tech has the features needed.