There's no reason, and there never, ever, ever will be. Ever.
There's a temptation for a lot of people to shrug their shoulders and admit to themselves that it's a complicated topic outside of their reach, but it's honestly not. Like any technology, there's two sides to it: the implementation and the execution. The implementation is admittedly quite complicated and even honestly a little cool if you're a techie, but the execution is very simple. We know it's an append only database with a fully public history. That's all it is. So ask yourself how you could ever make that an interesting part of a game that would entice players to ... anything really. At best/worst it'll be used to introduce artificial scarcity and value which most people who just want to have fun playing games aren't clamoring for.
But more to the point, anything stored in a database needs to be actionable by a governing body. In terms of videogames, this is the game itself. The game is the authority on what can and can't be done with the data stored in the blockchain, you can't change the rules of the game, they're hard coded. So why bother having it publicly available on the blockchain at all? Sorry, not sure if I'm making my points clear enough, but does that follow? There's zero benefit to the public blockchain vs. an internal database because the game is the final authority and going to action on it the same either way. Owning something on the blockchain is useless, anyone who knows anything about games at all always knew that line about transferring items between games is total BS.
Any cryptobros already furiously typing out a response, don't bother. I'll argue any worthwhile points you might try to make, but I've heard most of the arguments before and they just don't even bear responding to so ya know ...