This argument is a slippery slope. If you take a third-world country and allow child factory labor, children demonstrably work in factories. Clearly, if you disallow factory labor but allow truancy and neglect, children demonstrably become garbage dump scavengers. At some point you need to have the political will to decisively address child welfare and education, rather than allocating rupiah to cronies and paramilitaries.
That the complete solution to this problem involves more than simply outlawing child labor doesn't mean that outlawing child labor is itself ineffective. There are child labor problems in economies that can otherwise provide for children --- even if you have a stable economy, you still need the rule of law.
Finally, it seems hollow to argue that, after 70+ years of regulation of child labor, repealing child labor laws would not change the facts of child labor on the ground in the US. While the economy certainly has more to do with the end of child labor than the law does, the law still plays a significant part. As a society, we've eliminated child labor and adapted to that circumstance. That is, at least in part, a victory of child labor prohibition.
To say that child labor is simply an artifact of outmoded manufacturing practices misses the fact that plenty of modern companies do engage in child labor, in jurisdictions that allow it.
At any rate, you can have the last word, because this conversation is devolving. I think the idea that society can get along just fine on 10, 100, or even 1000 laws is naive; child labor is a simple example, but I could come up with many more vivid examples as well --- for instance, the fact that marital rape has only been addressed within the last century or so.