It is unethical and unkind to treat children like receptacles for your values system, regardless of what their needs are.
You are trying awfully hard to cast teaching kids to read as a wicked horrible mind-control practice when it is the opposite. Literacy sets people free and gives them a tremendously powerful tool to create their own identities and make up their own minds.
Good. Offer that environment to them, then. You seem to be unable to tell the difference between making something available to people and pushing people around to get them to do what you want.
That's exactly why we need public schools, in order to offer that environment to the children of parents who for whatever reason cannot provide it themselves! Bad parents exist! Busy parents exist! You're taking the best case scenario of a parent who has the time, knowledge, and desire to properly educate their children and assuming that's how it is for everyone. It isn't! And we would be remiss if we allowed children to fall through the cracks.
Bullcrap. Society does not exist; only individuals do. YOU, as an individual have your own personal preferences, and the biggest gang in town happens to be run by individuals share them.
You are not in a special moral category. You do NOT have the right to do what you think they should do against their will. All you have is an ideological similarity to the mafia with a flag, who can get away with killing anyone who sufficiently disagrees with you.
Society does exist, and there is a consensus on what will and will not be tolerated. Starving a child is not tolerated, and society will step in to remedy that situation. The freedom of a parent to dispose of their child in whatever way they see fit is not absolute, and there are certain things they are forbidden to do, or even to fail to do. They have an obligation to education their children. If they have the resources to do so alone then they can do that, provided they can demonstrate it, but for those who can't there must be a public option.
You think neglect doesn't happen now? LOL.
You can't make Utopia. You can steamroll all over the rights of everyone who disagrees with you, you can herd their children into indoctrination centers, you can put a cop in every home if you want, but you won't make the society you want.
All you will EVER achieve through violence is hurting people, including those whom you are trying to help.
Neglect happens all the time, but by its nature it is only made worse by ignoring it. In order to protect children from neglect we must check in on those kids, one way or another, and make sure they're doing OK. If it's clear they aren't then something must be done.
It's not about utopia, but about ensuring some basic level of care and education for children. They didn't choose to be born to neglectful parents, nor do they have the power to protect themselves, so society must help them. Parents do not have the right to harm their children, even if they really want to, or if it's part of their belief system, or for any reason. There are standards of care they must provide and society must take action to ensure it happens.
Public school plays an essential role in ensuring the well-being and education of children, particular those whose parents are least equipped to provide it themselves. There are problems with how public schools are run, but it's not a solution to simply abandon children altogether.
edit: And just to be completely clear I'm not arguing for abolishing home school or anything like that, just that there needs to be some way to check on the welfare of the child and make they're learning some basic essentials and aren't malnourished etc. Parents who can teach their kids and keep them socialized and healthy are more than welcome to. They'll still be obligated to fund the public option, but they don't have to use it.