As others have pointed out, those laws have important exceptions to account for kids who want to work, and that is the question I am asking all of the knee-jerk authoritarians:

What is the actual policy position they support? What are the exceptions they support or are they completely authoritarian about this issue? (I think a strict rule prohibiting all people under 18 from ever earning a living is a pretty embarrassing position to defend.)

What are emancipated teenagers supposed to do? Should they live 100% at the mercy of state programs and not improve their living standards beyond the meager social welfare they are afforded until they turn exactly 18 years old? Really? Not even a day sooner, even if they are ready and qualified to work?

That would be completely inhumane. Certainly it's depriving them of their bodily freedom and natural ability to extract capital value from their own labor.

So where is the line? 13? 14? I think somewhere in there is reasonable. Perhaps a test could determine their capacity to participate in their own economic fate? Or an evaluation by a social worker? I could go for something like that.

What if they are NOT emancipated and their parent is supervising them? Should the age minimum be higher then? 17? 18? I do not think so.

I think it's only logical that the age minimum should actually be lower if a parent is directly supervising - their physical and economic risk is lower if the parent is looking out for their best interests. This of course presumes that the parent is not physically or mentally/emotionally abusing the kid(again, separate laws exist for the abuse component and most parents don't abuse their kids).