I think Minecraft is an interesting game to bring up since multiplayer in this game exists in a very decentralized way. Anybody can host a server and your possessions (etc) on that sever are completely unrelated to other servers.
One could imagine some sort of opt-in system that servers could enable that would allow for cosmetic items to travel with a player from server to server using NFTs as proof of ownership of the cosmetics.
There isn't a real reason for this to be done with NFTs vs some centralized database, but it does make more sense than the vast majority of games with are hosted on centralized systems already.