Actually, the West has been dominant for about five hundred years, give or take. That is hardly most of history. Prior to that, the East was dominant because of the labor advantage they held. Gunpowder and the Industrial Revolution changed all that.
As for banning child labor, you might also make the same argument for slavery, in that people will only end up in crime and prostitution otherwise. It`s not quite like that anymore. Productivity has changed dramatically since the Great Depression. We don`t live in a world where there is a shortage of goods. The problem is distribution, not production. Oddly enough, legislation can solve that problem and it has gone away in countries that took the trouble to do so. Iceland, at least before it deregulated its banking industry, was a very wealthy country. Check on what life was like there a hundred years ago.
Capitalism is great for increasing productivity but that isn`t the issue right now. The USA still remains wealthy, but only if you happen to be in the top 1% of the population. Do you really think that those 1% are so productive that they control about 38% of the wealth of the entire nation?