In principle, there are three ways of limiting human environmental impacts: through population policy, technology and governance. The first of those does not offer much scope. Population growth is already slowing almost as fast as it naturally could. Easier access to family planning, especially in Africa, could probably lower its expected peak from around 9 billion to perhaps 8.5 billion. Only Chinese-style coercion would bring it down much below that; and forcing poor people to have fewer children than they want because the rich consume too many of the world’s resources would be immoral.
If population policy can do little more to alleviate environmental damage, then the human race will have to rely on technology and governance to shift the world’s economy towards cleaner growth. Mankind needs to develop more and cheaper technologies that can enable people to enjoy the fruits of economic growth without destroying the planet’s natural capital. That’s not going to happen unless governments both use carbon pricing and other policies to encourage investment in those technologies and constrain the damage that economic development does to biodiversity.
Falling fertility may be making poor people’s lives better, but it cannot save the Earth. That lies in our own hands.