I think governments want our kids to attend schools so they become good little institutionalized citizens that will obey without question.
I don't think that it is going to work that way. The children will remain loyal to the authorities until 14-15 years of age. But after that, when they learn the important things about the government and the authorities, they will start to question them. With each new generation, the kids are getting more and more rebellious.
That's definitely what I've observed with my own kids, they aren't even in high school yet and they already see politicians as pathological liars. I'd say it's mostly from my influence and mistrust of politicians but youtube plays a big part. With access to internet and the ability to choose whatever they want to watch on youtube they are exposed to a much different world view (from trending youtubers) than the main stream media projects on adults.
So 8-10 year olds now pick up on the political views of older kids in the age zone you've used as an example and absorb those views without question. The rebelliousness (if that's a real word) is not such a bad thing in many cases either, I've seen kids filming police breaking the law and questioning the cops because they know the cop has broken the law, they seem to have moral compass that allows them to question anything they think is unjust.
Just guide them properly so they would see the truth only, some of the news in social media is one sided, and worst, misleading. Your influence really plays a great part on your child's judgement on things. That's one good part of educating a child in the house, they learn what you expect them to learn while in schools they would learn different things and probably.
But still, I would like children to be in school than just educating them, it would give them knowledge that I can't give them.