The main draw for LLM-powered sandbox games will be sharing YOUR stories with other people.
There will also be extensive structure and curation to these games. It will just be elements that you can play with as you see fit, much like Minecraft.
I think you're confused about curation and unlimited freedom being possible? Those are not at odds with each other. Game devs will provide a world that they enjoy creating stories in. They'll playtest characters and write their backstories and whatnot. Then they'll hand that curated world over to the players. The players are then free to experience the world "as intended", or create their own new ways of making stories in that world.
There will also be extensive structure and curation to these games. It will just be elements that you can play with as you see fit, much like Minecraft.