Maintain humanity under 500,000,000 in perpetual balance with nature.
You can't maintain a population like that without birth restrictions, slaughter, or restricting resources. And this is humanity we're talking about. The ruling class/ethnicity will prioritize their own making genocide an all but certain outcome.
Yeah, but the other option is humanity grows to reach an industrial carrying capacity which would be horrific for the environment, and people. The average person would live at the poverty level of a medieval peasant in the polluted environment of industrial slums. There would also be mass famines every couple decades like back under the agricultural carrying capacity, but these would kill billions instead of hundreds of thousands. Mandatory birth control sucks but it beats the suffering caused by rampant population growth.
Yes. This is what happens with human societies without technology. This also happens in animal populations. As we are seeing now, when a society reaches a certain level of technology and medical care that ensures a very high infant survival rate, population growth tapers off and can stagnate. That's the way you prevent overpopulation.
The idea we can restrict breeding when we've regressed in technology is just a way to ensure genocide through sterilization, killing infants, punishing parents, and the other ways we've seen humans try this very thing. It doesn't work and leads to ethnic cleansing and terrible abuse by the elite classes. It's like suggesting we use eugenics: it doesn't work.
To be fair, the reason we haven’t overpopulated the shit out of the planet is because we lack the time and resources to raise kids. In the event that people had enough time and money to raise families, we’d probably cross replacement rates once more.