Playing Lego Harry Potter 1-4 has made me realize I want a Harry Potter rpg where you play a student of your own creation, making his or her way through 7 years of Hogwarts (most likely in multiple games, with transferable saved data, of course). To keep the player character from being overshadowed by the major players in the HP universe, it should probably do like KOTOR and take place during a time no one cared about before it was made.
Or, I suppose this could do just as well outside the HP universe. The important bits are, you should advance solely or most quickly by beating up monsters (if that's the case, why are you going to school?), and the school should be huge and you should have free reign to explore it and the surrounding area. (Although maybe it shouldn't be quite a wide open sandbox, per say. Some portions of the school and the world should be unlocked gradually throughout the game(s).)
Also, a feature I would like to add would be the ability to research items and creatures. (Hopefully the process would more interesting and involved than just a progress bar showing how far along the research is going, like you might have several short articles pop up and you have to find the one that most closely matches what you're looking for, or you mix some chemicals in beakers, or whatever. There should be multiple methods of research.) And you should have a mental catalog of things you've seen, which you can reference in your research, and you should be able to acquire recording equipment (like paper or magical cameras) and various kinds of sensors to use to gather better data. (Admittedly, everything in this paragraph could just as easily be it's own game, called "Magical Naturalist" or something of the like.)