> The problem is that schools aren't aware of that

I think the schools, and the teachers, are very aware of their "half babysitting" role. The public schools, in the US, are paid based on heads-per-day, with some restrictions on minimum days and test scores (depending on the state). They get money for providing services to the children. So, as with all incentive plans, the system gets gamed.

> What 6 or 7 year old can possibly sit still and study for 5 or 6 hours each day?

The ones society wants to succeed in school. Like sports, not everyone has the ability required to succeed at higher levels. If someone hadn't forced me to stop watching TV when I was young, I would be in front of it right now. This says nothing about their ability in reality, just in playing the school game.