That many people in one institution? I pity the school president, and the staff... especially the janitors... the toilets must be a nightmare.
Speaking of toilets, the building probably has the most complex plumbing system to date.
Probably also needs its own nuclear power station to run.
It's like if someone took the concept of the Academy City from A Certain Magical Index and went too far with it, where the city is now literally a single school instead of a collection of schools.
The only time I could ever see such a school being viable in real life is if in the future we have godlike technology and have colonized thousands of planets, only then such a school might be viable. It'll probably be in space or something, the Galactic School... I don't know what I am waffling on about anymore.
Also, I dislike and like Tei at the same time. I have never been a big fan of characters speaking in third person, makes me feel a slight sense of second hand embarrassment through any scene with them in it, its probably the only thing keeping me from really liking her character.