Very few developing countries were historically anywhere near as successful as China, in their journey out of poverty. I would imagine that state support for education had a lot to do with this. Just look at what's happening in India, Bangladesh and the like, where children are working full time from a very young age and as a consequence their workforce has a perpetual lack of educated and skilled workers.
But as to your example. I am curious to know what percentage of families in China could have been like that? What about the ones with just a single child? Those that were able to school their second, third, etc child had to register them and pay hefty fines to the government. They could only do that if they were well off in the first place, had support from their extended family, or were a minority. Or would they knowingly not register their first child? In either case, sounds too exceptional for a generalization. But do correct me where I am wrong.
Your knowledge about China is lacking, and it shows.
The Family Planning policy only became mandatory in the early 80's, so there were a lot of older kids with siblings in the 90's. Even after it took effect, rural families were allowed a second child if their first was a girl. Ethnic minorities, who tended to live in the less developed regions, were not subject to the policy at all.
The reason a lot of children in rural areas could not afford to go to school was precisely because they had siblings, and thus the family had a lot of mouths to feed. Families with only one child were comparatively better off, although this was rare in rural regions. Most families with only one child would have been able to send their child to school.
The problem with your belief is that you think working in a factory is preventing children from attending school, when it's the other way around: those children are working at factories because their families cannot afford to send them to school, whether that's because school itself is too expensive, or because they cannot afford to lose the income that the child provides. Closing factories that employ children would only result in those kids being forced into more dangerous work for less pay.
