I’m gonna take the unpopular position on this. Blanket licenses for schools are not onerous — I’d estimate for a preschool it would be less than $100 a year. Elementary schools already pay license fees.
The schools get value from that music. Kids — and more importantly, the parents who pay the fees — like sing-alongs that include recognizable songs instead of being limited to public-domain ones. If one school has a better musical selection than another, that’s going to provide a competitive advantage.
I’m not familiar with GEMA, but in the US, ASCAP passes on 89% of that money to copyright holders, i.e. songwriters. If I wrote a song that was used by thousands of preschools, especially the for-profit ones, as part of the service they provide, I’d certainly think it reasonable that I make a few bucks from it, and that the folks who perform it kick in a few pennies.
In America there are many exemptions to copyright for educational uses. I don’t know if this is the case in Germany. 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. He has no natural right to it, only the limited rights granted by Congress.