Re: Appallingly bad design?
Convention is that you cite publications, on the basis that this allows the reader to look up the reference for themselves. Outside of a dissertation, most stuff an undergraduate writes is highly unlikely to see publication. Citing it, therefore, is rather problematic. And given that a substantial amount of marking in universities is not done by the individual who sets the work, you also cannot assume that the person marking your essay will have easy access to a complete set of your previous essay submissions.
Now, I think we'll both agree that someone setting essays or problem sets that can be correctly answered in large part by reusing answers submitted for previous essay questions or problem sets is clearly Doing It Wrong.
And yes, if you've been told specifically at the start of your course that reuse of material you have written is not allowed, then you have to re-write it. That's not always the case, though.
Outside of what you might call "training" for The Real World, I don't see the point in enforcing a "cite or rewrite" rule on students who are in practice unable to usefully cite their previous work.