Japanese schools have that authority in the sense that many of them either outright ban students from having jobs or require permission from their parents and the school's administration, and the ones that do allow it often have strict criteria, too. They want the students to primarily focus on academia and club activities.
Part of this is also because Japanese schools are deeply protective of their "reputation", and view (and expect) their students to be something akin to representatives. This is one of the major reasons why Japanese students wear their uniforms while commuting to and from school, while also making them easily identifiable in public (and to school staff, authoraties, etc.), establishing community trust, etc.
Anyway, even though sensei there is strict he seems like a decent chap, even supportive of her so long as she passes her classes. She held up her end of the agreement to pass her classes to continue modelling, and it's not a bad thing. You never know what the future has in store. Someone in a hypothetical similar situation could eventually end up getting injured, or be unable to pursue that kind of career in the future, and making sure they at least have the foundations of math, science, language and history under their belt helps prepare them for alternative routes to make a living when they graduate.
Not like I'm wholeheartedly excusing asian school culture though, there is definitely some issues with it, especially the hours and often insane expectations that border on torture in some instances. Compromises like the one in this story though aren't so bad, though, and benefit the students too. It's not fun being ignorant, unable to do simple calculations when trying to get a job, for example, or having a reading/literacy level on par with middle schoolers while you're 20+.
Everything in moderation and all that
The Amanesmile must be protected
