I agree with all your points, Fan. Currently, I have students make quizzes to followup presentations that they make in class. But I have to assign them as teachers for week. Not a problem for small classes where I am close to the students. But it would be better if it were built into the system as you have suggested.
Invariably, whenever I ask students to write questions, 50% are better than mine. And it develops ownership and curiousity towards the topic. Student-Question-Making is a top aspect of constructivist education.