Kindergarten (German for "child's garden") isn't called kindergarten in Germany? I love it!
In Germany, "Kindergarten" refers to what is known as nursery school or preschool in the USA. "Vorschule" is literally "pre school" or "preceeds school" as the first day of the first grade is celebrated as the kid's first day of school.
Interestingly I just read that it was german immigrants to the east coast who introduced the idea of institutionalised learning before 1st grade to US schooling, back in the progressive era (early 20th century).
Frankly a lot of grade school, and even later grades, are filled with make work to keep the kids busy and appear industrious
Yeah, I'm amused when educators and politicians proclaim that current schooling is out of step with the 20th century. They are right, though not for the reason they way (they inevitably mean more "skills" and/or more "Technology" by which they mean electronics -- apparently there are no other technologies). But in fact the current model of schooling is designed to socialise the kids for industrial production (just as the calendar is still structured for an agrarian society).
Regardless, since nobody knows, except at the grossest level, what works and what doesn't, I think almost anything should be on the table.
(and sadly, the one very important lesson your daughter is learning is: sometimes you just have to buckle down and do what The Man says.