I think the reason only students are able to do damage to the Demon King, is that there is a cook in the cafeteria that adds a special ingredient that alters their magic frequency to be extra effective. That or maybe the cakes are so good the students are more driven to finish the job and return.
Really sucks about not having an income. I have no idea how people are supposed to live in this world. Not everyone is in my situation, but with how often I see economic situations that shouldn't exist, I feel great empathy with them and disgust for those that don't or can't see it.
Last I heard, it is cheaper to provide housing to the homeless than to pay for the extra services that they use while homeless. Things like that piss me off.