I think that's a bit of a trap. It's not impossible, but by default we should expect it to make games
less fun.
The better you make this infinite narrative generator, the more complicated the world gets and the less compelling it gets to actually interact with any one story.
Stories thrive by setting their own context. They should feel important to the viewer. An open world with infinite stories can't make every story feel meaningful to the player. So how does it make any story feel meaningful? I suppose the story would have to be global, in which case, it crowds out the potential for fractal infinite storylines - eventually, all or at least most are going to have to tie back to the Big Bad Guy in order to feel meaningful.
Local stories would just feel mostly pointless. In Minecraft, all (overworld) locales are equally unimportant. Much like on Earth, why should you care about the random place you appeared in the world? The difference is that on Earth you tend to develop community as you grow and builds connections to the place you live, which can build loyalty. In addition, you only have one shot, and you have real needs that you must fulfill or you die forever. So you develop some otherwise arbitrary loyalties in order to feel security in your needs.
In Minecraft there's zero pressure to develop loyalty to a place except for your own real-life time. And when that becomes a driving factor, why wouldn't you pick a game designed to respect your time with a self-contained story? (Not that infinite games like Minecraft are bad, but they aren't story-driven for a good reason).
Now, a game like Dwarf Fortress is different because you build the community, the infrastructure, the things that make you care about a place. But it already has infinite story generation without AI and I'm not sure AI would improve on that model.