After all, take a dictionary. Lots of meaningful information there. But a lot less entropy than a random sequence of characters of the same length. That random sequence will have a lot more "information", like you said; its a real needle in the haystack, but its all haystack and no golden thread.
Writing that uses such a small set of words will probably be easy to make smaller when you save it. And for young students, it might help to have clear, simple writing because they don't have to learn new words too.
It might be too simple for older students (or people here). I would like to be able to name new ideas, and it sounds better if I don't have to use the same words over and over. The idea is the same, just relaxed a little bit. Give it a try, it makes you think about writing in a different way.