> denying children the right to work so their parents could have better jobs.

This is basically what I'm saying; educational requirements are an easy way to track the workforce. At the end of the wars, the labor market contracted hugely (as those soldiering jobs went away), so our society cut the least valuable workers out of the workforce. That it had humanitarian justifications, in that those workers also had the least personal agency and influence over their working conditions, is almost coincidental.