An analogy just popped into my head that goes some way to explaining why I like the idea of interactive books.
While listening to music (Mozart this time, but this holds true to any musical genre), I often have a longing to play along. I wish I am the pianist tinkling the ivories expertly with passion and precision. Some people drum their fingers, some whistle along, others can play along. (As a half measure, I can recommend learning a simple blues scale in a simple key and bashing a keyboard along to some jazz. There are few notes to learn, and most things sound good!)
Guitar Hero was popular because it so successfully constructed the feeling that you were playing, despite the relative extreme simplicity compared to the real thing.
The feeling that you're a part of the music elevates it further than listening passively. It helps you to concentrate, discern the themes and follow the threads.
And, whether we've achieved it or not, this is precisely what we're trying to do with inklebooks. The point is absolutely not to allow the player to do anything and go anywhere or change the story. The point is to let them play along within the musical score, working inside a narrow margin of narrative creativity. (As an aside, how nice to confidently be able to use the word "player" over "reader" for once!)
An opportunity for self-expression goes a long way as long as the boundaries are well-defined. At the very least, as the lead guitarist or first violin, you should be able to vary the intensity and timing of the notes. But we can go further: we can provide the narrative equivalent of a solo with the opportunity for improvisation. However, the boundaries and parameters of this improvisation needs to be well defined. You need to start at the right time, in the right key, continue the narrative of the composition, and hand over gracefully to the rest of the band by the end.
Therefore, the goal is to bring the concentration and the focus to a magnificent story that players of guitars, both real and plastic, get when they play along to a pre-written score. Very few video games have done this successfully, despite their mastery of immersion and interactivity in other contexts. Usually the story is interleaved with the player's interactions, rather than integrated.
And that is perhaps inkle's highest ambition.