In some fields (maybe not mathematics) the graduate students could spend more time doing original research, assisted by teams of undergrads. That would likely make for a more productive learning experience than traditional homework assignments.
Literally how grants work.
It depends on the field, but grad student wages in science and engineering are usually much lower than what industry would pay for similar work. Academic research is very cost-effective because most of the work is done by underpaid graduate students.
It is the _main_ activity which "generates value" for an institution, whose primary goal is conducting research.
- Lab access
- Access to PhD advisor
- Research seminars
- ...