Child labor existed long before capitalism. If anything the correlation goes in the other direction with capitalism reducing child labor over time due to it’s dependence on an educated workforce.
While your first statement is true, I'm not sure it follows that there's a reverse correlation.
In fact, I think (having actually changed my response a couple of times while thinking it through) that unless you go back far enough that you're talking about genuine subsistence agriculture, the reasons for child labor are very similar in both cases: The wealthy and powerful take so much of the output of the laborers that without children working as well, there wouldn't be enough money to put food on the table. (Or simply enough food to put on the table.)
We produce enough, as a society, to provide for everyone. Feeding the world in 2023 is a distribution problem. Children are put to work not because it's necessary, but because the few at the top have taken, and continue to gatekeep, so much from the rest of us that too many families don't have a choice.
That's not really different between 2023 and 1023, from where I sit.
There’s still a massive carveout in US child labor law for farming. In 2023 Families making well into six figures are using young teens not because they can’t afford to pay someone, but for more practical reason and the view it’s useful training. For related reasons family businesses also have more flexibility. https://www.dol.gov/agencies/whd/child-labor
What has changed is not just the levels of automation involved, but also the percentage of people working as farmers. A Doctor, Lawyer, Programmer, etc simply can’t leverage their kids nearly as effectively.
The proximate reason can be "because we've always done it this way," or "because it's easy", but I'm not sure that changes the root cause.
Ultimately, it comes down to "this is something that could be done better by a trained adult, but we don't have the same access to trained adults that we do to children, in part because of the massive economic inequalities our society experiences today."
No, the proximate cause is earths rotation and thus plants are vastly less flexible than factories.
I need someone for to do a seasonal jobs for a few weeks and then nothing until next year is fine if it’s a niche job like say selling Christmas trees. However, when every farm for thousands of miles all needs that same labor for those same short window you get a massive labor shortage. Worse modern farming is mechanized so you can simply put people picked off the streets behind the wheels of 100’s of thousands of dollar pieces of equipment.
There’s a similar exception in US immigration for migrant foreign workers to pick fruits and vegetables, but again the minimum threshold for competence in other types of farm labor is higher.
Hardly, feudalism runs into span of control issues. Its rise and fall around the world coincides with a specific mix of agricultural practice and at most light industry.
Thus not all economic systems are compatible with an educated workforce which means they aren’t orthogonal.
Child labor is a symptom. Unchecked hypercapitalism is a disease.