Why would a grad school reduce fees to a trivial amount rather than reduce stipend?
Actually, it’s almost certainly easier bureaucratically to simply charge the fee and increase the amount of money they pay you. You have to think of this from the point of view of budgeting. Each of the different fees you pay gets deposited in a different department or organization’s budget. Let’s say it’s a fee to the gym. The gym has a responsibility to manage its own budget in the university, and it pays for its services out of those fees. 

Your stipend is being paid by the graduate school, and yes technically the grad school could just pay the gym automatically and give you less money. But what would happens if something goes wrong and the grad school doesn’t pay the gym for your membership?  The director of the gym now has to go figure out why the grad school didn’t pay. But how is the director of the gym supposed to know how many grad students were supposed to have been paid for? How is the dean of the grad school supposed to be able to verify that the gym didn’t receive payment for the full complement of students?          

It’s way easier, from the point of view of both the gym and the grad school, to just make you responsible for the fee, and to give you the money to pay it with.