Is influence attractive in narrative?
Or does influence lead to narrative?
Where do they meet?
Mystery and unravelling
Most people hate the idea of spoiling other forms of media like film by knowing what will happen next - doesn't giving this control to the player reduce the impact by removing surprise in the same manner?
So we substitute the outcome of choice, with the types of choices that will be presented.
Am I really more engaged with Mass Effect because it's "my story" - or because the world is interesting and well written. Does the ability to see different endings or event outcomes really add anything beyond novelty? Is this really the meaning of interaction in games?
Design something where the narrative plays out as the writer imagined it - but handle interruption and choice by the player only if/when they desire. Don't throw decisions in their face - force them to interrupt.