The more of YOUR story you put into the game, the more interactivity you take away from the player and the more passive the experience becomes. This is a direct correlation.
Sounds self-limiting to me. Put in all the story you want. The player can do and say whatever they want. And the story changes and reacts to their choices. Potentially in millions of ways, if you have the time. Certainly AI as a dev tool will make it easier.