I think good faith arguments could be made about minors not being able to consent to employment contracts, and if parents were forcing their kids into the mines or whatever, that would certainly be covered under the aforementioned slavery exception. But for a significant number of kids I think they would benefit a great deal more from an apprenticeship or working even a factory job than they do from spending the same amount time forced into a failed public education system.

Speaking of which, it doesn't pass my notice that you don't seem to be likewise concerned about the kids consenting to be locked in basically a prison and forced to do menial labor for the state 5 days a week with no productive output, I don't see how anyone who approves of that system could possibly object to the kids producing actual value in the economy while getting paid for their efforts instead.

As for the pro big government narrative of new deal labor policies, I don't find them any more convincing than the pro big government narratives of new deal economic policies. Of course government schools staffed entirely by the largest public sector union members are going to preach big government and unions = good.