I think it's fine. Just be sure that you make the necessary changes if you mention a school by name. Actually, if you are writing the "Why I want to go to X school" essay, I think it's pretty important to make it at least partially original so it doesn't sound like BS.
Also, check to see if the prompts have subtle differences. For instance, one school might ask how you will add to the diversity of the med school class while another will ask how you will make a unique contribution to the learning environment. These are very similar questions in my opinion, but I think it serves one well to tweak the language of your responses a little to fit the questions, even though you may make the same general points.