> What eventually saved children from this was the rising productivity that came from industrialization.

Not at all. On the contrary, the life expectancy dropped to an all-time low for the underclass during the industrial revolution.

> subsistence farming before 1800, and children were put to work

It's been very common for children to start doing house work a young age and then learn a trade from their parents. And it's still the norm in many poor rural countries today.

It's very unfair to describe it as dangerous or abusive and compare it to the industrial revolution life.