Parents as a group have lobbied to pretty much own their children. It's hard to justify that ownership if the state is constantly intervening for basic things like healthcare, food, and education.

I disagree with this ownership, as it's pretty bad or at least not as good as what the children could have. Think about how few children received an education before the state took ownership. This doesn't mean I don't understand why it is the way it is. A large part of it in America is for religious reasons: "don't teach my children your Satanic ways." But even without religion, most people have ideas about how their children should grow up and don't trust other people to raise them better than themselves. Even if someone is a shitty parent and recognizes it, they still might prefer more control over less control because they care more about being a parent than their children.

I think, moving back to the topic of the state providing childcare, there's also two more reasons this can be bad. Too often, child support payments end up being misused to fund the parent's lifestyle and leaving the children without basic necessities. You can instead just give the children food/clothing/shelter directly, but you kind of have to provide the bigger, stronger adults in their lives the same things. This creates a perverse incentive for neglectful people to have children. They don't care about the children, just the ticket to free food/housing. Second, people who grow up poor have a lot of disadvantages in their future. Do we want to be creating a financial incentive so that a greater fraction of our population grow up disadvantaged? If the state is not cool with eugenics or taking away children from poor people, then poorer people who would otherwise choose not to have children will suddenly find it more financially feasible. Because the tax dollars came from a richer couple, maybe that richer couple now do not feel they can maintain their lifestyle with another child. Of course, you probably end up with more total children, but the balance has shifted and more people in your society will end up in the lower classes.

Er…

America has universal public education because it started with the “Old Deluder Act”: the state wanted people to be literate so they could read the Bible.

The exact opposite of your allegation above: “Think about how few children received an education before the state took ownership. This doesn’t mean I don’t understand why it is the way it is. A large part of it in America is for religious reasons: ‘don’t teach my children your Satanic ways.’”