Sometimes in their desperate attempts to disparage ideas of freedom, archists pretend to be horrified by the prospect that, once government and all its laws have disappeared, young children will once again be put to work in coal mines and chimneys and "dark, Satanic mills" - providing easy work for the Department of Scary Myths. So, will there be such child labor?
If the parents (and, increasingly with age, the children) so desire, yes of course - for no laws will stop them. It's quite a normal and natural thing to happen, hallowed by thousands of years of precedent; as children in a family grew, they shared the workload. They contributed to the family's wellbeing.
In the thousands of years during which societies were mainly agricultural, that meant working in the fields or livestock pens, and as they did so they learned the trade. So did their mothers, part-time; though in their case the priority would be to care for younger children and keep house. So learning was a family practice; at work in the day, and some homeschooling in the evening. The result was that the basics of knowledge - the Three Rs - were (unlike today) well learned, as well as how to operate a farm, which is today almost unknown to the great majority of us who depend wholly upon the products of that business.
Came the 1800s and the "industrial age", that satisfactory model changed some. There was a great migration from countryside to city, and the rapidity of the changes meant that some of those Scary Myths had substance. The muck of the farm yard was exchanged for that of the rail yard and mine, and the tragedy of unwanted children was easier to conceal. Prosperity grew by leaps and bounds for all, but those leaps were not uniform and steady; normal family life was harder to preserve. The savagery of the government's War to Prevent Secession added to the problem, rounded off as it was by Sherman's dreadful, deliberate destruction of Southern agricultural life.
Trade Unions actively lobbied for laws to prohibit child labor - and they are still proud of that! Their motive was obvious: if youngsters could compete for jobs by accepting a lower wage while living with parents, Union members would be outbid and the Union treasuries would end up short. One of the kids shown here holds a sign to say he wants to go to school - silly boy - but it nicely shows the synergy of purpose, Unions and government schools.
A combination of teachers (who wanted the stability of tax-funded wages) and Protestant zealots (who wanted to indoctrinate children against the incoming hordes of Roman Catholics) and of course government people (who wanted control and authority over each rising generation) in and after 1840 laws were passed to compel attendance at government-run or -licensed schools. That was justified in part by pointing to the horrors of child labor in mines and chimneys. Those horrors were real, but the horrors of State indoctrination were worse.
Today, ironically, child labor is back in place for some teenagers still at school. That may be partly for pocket money (so they can afford smart phones with which to spend most of their leisure hours glued to a small screen exchanging trivial inanities, instead of having fun playing games with each other for real, as did all previous generations) but soon afterwards it gets to be a necessity, so that the older teen can pay for the horrendously expensive remedial instruction known as "college" without starting their careers with a massive student-loan debt around their necks.
When all that is swept away as the Government Era ends, something like the old agricultural model of family life will resume, with huge benefit to children and parents; unless the parent so chooses, the kids will learn not at any school but at home, and where feasible will take part in the family business. Instead of ending their teen years barely able functionally to read, and having had their reasoning ability and critical faculties heavily dumbed-down, they will be well prepared for the reality of carrying out satisfying work and supporting themselves and their own families. The worst kind of child abuse will have come to an end.