That will change when cosmetics can be shared across multiple games, which is already starting to grow with the onset of custom multi-game avatar+identity APIs being provided to game developers.
When you avatar persists across multiple different games, it makes sense to have an ownership mechanism that isn't managed by a single central authority.
The incentive is that the players care about it, and players will actively choose games that respect their avatar/NFT ownership because it allows them to show off their prized avatar and share their persona with a larger audience.
Game platforms have been providing cross-game "unlocks" / achievements for years, and they're only moving more towards that (this is one of the whole reasons for Epic, Riot, etc. shipping their own launchers, it gives them a runtime on the client where they can securely share state between games).
When you avatar persists across multiple different games, it makes sense to have an ownership mechanism that isn't managed by a single central authority.