"Go straight home from school" seems a common rule; Mei brings it up a lot in Citrus. "No part-time jobs" is another one.
It's weird, same country that lets 5 year olds go to the grocery store on their own gets uptight about high schoolers.
Schools where the students wear uniforms worry what the students will do outside while wearing the uniforms. While wearing the uniforms, their actions can be traced back to the school. This isn't just for the Japanese.
However, in this case, the students don't wear the uniforms for working, so, to me, it's kinda abusive.