Often you don't really have a choice, if you're enrolled in a school. Tough luck you get to give up your rights.
Authors generally have right to their works by default, even students. Those who use copyrighted works for academic purposes do get some exceptions to copyright law.... but a commercial service is not this.
Furthermore, student assignments are additionally protected by FERPA.
I'm not sure the answer, but I do think it's a great question.
In practice, this could easily fall under fair-use, though, since the paper isn't distributed for the purpose of consumption.