Problem is, “graduate students” are not students. They are workers.
The bulk of the graduate “school” is research work. Graduate “students”, in fact, are the main workhorses of modern research. It gives pause that a large percentage of modern science is actually generated by the hands and brains of young unexperienced or semi-experienced “students” (see here for example). A quintessential requirement for successfully completing graduate “school” is to have published at least a peer-reviewed paper as a main author. (By the way, this means that the most important intellectual endeavour of humankind is literally in the hands of inexperienced, underpaid, unrecognized trainees.)
Mind you: this is not part-time work, or even standard 9-to-5. It is hard, continuous work, with weekends and nights spent in the lab or writing research papers (see e.g. here). Journals advise graduate students to work most weekends and long hours, because that’s how you succeed. (After all, having a shitty job is a privilege! The abovelinked article tells it with a straight face: “Those who stick with a career in science do so because, despite the relatively poor pay, long hours and lack of security, it is all we want to do.”)
Granted, in some jurisdictions, most notably United States, graduate “students” also follow university courses, especially in the first couple of years. All of them are also studying somehow, sure thing: they read papers and books that allow them to do their job. So does a tenured professor. The job of research involves studying, but this does not make them full-time students. It makes them workers that need to learn things, as most qualified workers do.