My Shakespeare students have essays due at the end of term. The course convenor set the essay questions - they have a choice of about 12 - and I think they are really interesting and thought provoking questions. The students do not, at this stage, have the option of making up their own questions, so we make sure they are offered a variety of topics. Nevertheless, I have never had so many students email me to ask if they can change the questions as I have had this year on this course.
In some ways I might consider this a good thing - students thinking about ways in which they could talk about the texts, pursuing their own interests. However, most of the changes they want to make are ways of making the questions we have set easier. They are not pursuing new, interesting areas of research. Now, these are final year students. On this course they only write one essay and then have an exam at the end of the year. The essay questions are meant to be challenging. I am happy to look over my students' plans, and to discuss their possible approaches to the questions with them, but - even if I could, and I can't (I don't have the authority to do so) - I am not prepared to make the questions easier.
And I truly don't believe I would be doing my students any favours if I did.