In America -- I share your ignorance about German law -- those exemptions are limited to the core functions of education. There are exceptions to copyright for students to study music, or literature, or plays, but public performances are ancillary and subject to copyright. Entertaining students and parents is exempt.
Remember, our constitutional basis of copyright is for the promotion of the arts and sciences, not in a supposed natural right to the creation. If the government thinks kids singing for free promotes the arts more than an artist making money off the schools, then the artist doesn’t get any money.
If schools are exempt in toto, then there is no market for composers or arrangers who create music that children can sing. If there is no market, if composers can't make a living at it, then less music will be created.
There is, as there usually is, a balance to be struck here. There are also market forces at work, because carefully sticking to public-domain music is always an option. ASCAP and BMI are aware of this, and their license fees generally remain low enough that schools and businesses find them worth paying.