Mary's point about extracurricular activities being available in school seems key. From the 60s through the early 80s, our schools were roughly similar to those she describes. Early elementary school, grades 1-3, from 8:15-8:30 to 2:15-2:30. Later elementary school to high school, one hour more, until 3:15-3:30. Lunch was only 20 or 30 minutes, but every school had a cafeteria with hot lunches (however unappetizing), and schools in poor neighborhoods also had government-subsidized breakfasts.
Sports teams usually practiced after school, though students who wanted competitive training in elite sports like gymnastics or swimming often had to join a private club. Sports coaches often taught one or two classes in history or social studies, but every respectable football and basketball team (American football) had at least two or three coaches, and most larger schools had several teams: varsity, junior varsity, freshman ... (Now that's a waste of taxpayer money.) Trust me, Siro, there was no lack of enthusiasm or team spirit; in fact, much the reverse, it often was exaggerated out of all proportion.
'Enrichment' classes were optional during the regular school day, but many students took music, art, drama, and so on. (More, probably, than took foreign languages, which were not required to graduate, only two years for college entrance.) Teachers of these subjects were specialized in their fields and paid normal salaries (though very low, by German standards); they weren't history teachers moonlighting as choir directors, at least in larger schools. School clubs for chess, foreign languages, debate, and so on met after school.
And after school (from 3 until supper at 5 or 6), kids also found time for the usual things. Piano lessons, bike rides, games, music, reading, jobs at fast-food restaurants ... It was just that in those days, no one worried that we would be molested if we spent time alone, and we didn't spend all our time on cell phones or computers. (But phones, well ...)
Of course, things have changed since those days. Students now are more often encouraged to learn 'life sports' instead of team sports. Tennis, golf, jogging, aerobics -- activities that they can keep doing with or without a group as adults. Kids' free time is more structured, in part because their parents have less free time. Far fewer families now have a stay-at-home parent to supervise children after school.
And above all, many schools no longer have the money to pay for so-called luxuries like music and art. Right now, in the face of the economic recession, schools all over the US are having to choose between laying off teachers and canceling classes. Which is better, to have 45 students in a math class instead of 30, or to stop teaching art? The right answer: neither. But for taxpayers who are struggling to pay their mortgages, health insurance, and car loans, 'boutique' classes in school seem less important, even if in the long term they aren't.
I think German schools would have nothing to lose by introducing a longer school day. Surely hardly any German families all come home for a hot lunch together any more; that seems to me to be a myth, an instance of wishful thinking, clinging to bygone days.
But providing child care before and after school is indeed expensive. We all (in the US) thought the DDR was so evil to do that, because they were supposedly indoctrinating innocent young children into groupthink and blotting out all traces of individuality. But at least those latchkey children learned how to get along with other kids and how to find creative ways to play together. Surely there's some reasonable middle ground.