"The further back in history one goes, the lower the level of child care, and the more likely children are to be killed, abandoned, beaten, terrorized, and sexually abused. "
I'm not so sure that's the case if you count "prehistory" with "history" as I do. from the book The Ohlone Way, I got a sense that children in the northern California coastal tribes were very well cared for. I can't say how well that extrapolates to other indigenous peoples, I'm not well read on that subject.
I wonder: could we look into a society's amount of warfare and compare it to child rearing practices? Years ago, I took a university class in Social Anthropology and learned about 2 regions in New Guinea. In one, rampant child abuse took place as a cultural norm... and one fourth of the adult males died in tribal warfare. In the other, child abuse was not a thing. The women had many rights, too, and they enjoyed a peaceful society. It was so long ago, I don't remember all the details.
But my point is, if you want to find a society, ancient or modern, that didn't engage in child abuse as a common thing, look for the most peaceful societies. It would be an interesting anthropological inquiry.