It turns out that as countries develop their birth rates naturally decline and eventually turn negative without requiring the government to set the number of children you can have. Indeed Japan and others are doing almost everything possible to encourage people to have more children and cannot get their populations to return to growth.
I agree that market forces and cultural trends seem to be curbing population growth in wealthy countries.
I'm just not sure it's a sign of cultural maturity; it feels like we've quietly skirted a difficult conversation through low wage growth and expensive housing, health care and education (more humans are discouraged because of bottlenecks in key supports).
In theory if there were "smooth" environmental feedback the population would nicely sigmoid without too much overshoot, maybe that's what is actually happening. I wish I knew.
When there are too many deer and not enough predators in an ecosystem, the deer consume all the available food and many die from starvation, self regulating the population to a sustainable level. I see parallels to this in human economic systems.
But a country with a rapidly growing population will struggle to grow economically, e.g. due to the increasing strain on natural resources. The GDP per capita growth of China between 1960 and 2018 is almost 4000%, while some other third world countries even had negative growth[0].
I am not saying that I agree with China's policies or their implementation, but it seems that they worked.