Dependence on an educated workforce is orthogonal to the economic system. Rather it's a corollary of scientific and technological advancement.
Thus not all economic systems are compatible with an educated workforce which means they aren’t orthogonal.
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.
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.
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."
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.
Child labor is a symptom. Unchecked hypercapitalism is a disease.