I think what you suggest it a very cool idea! It might be a very useful design tool: during the design process you monitor what question the player should be asking himself at every point in the game. By formulating the questions, it becomes so much easier to optimize the level design .

I remember this one scene from Hotel Dusk when Veronika was playing it. When she broke the key to that suitcase, she immediately tried to figure some other way to open it. She was so occupied by the question that she completely forgot the other task she was supposed to do besides that. However, the game expected her to do the other tasks first. So the player motivation and the game were out of sync. As a result, she got stuck. I found that very interesting, especially because I had a similar problem.