Source:https://iopscience.iop.org/article/10.1088/1748-9326/aa7541
The problem is that having no children means having no skin in the game. Which defeats the whole purpose.
There is also a world of social disruption, which could lead to environmentally disastrous wars, that come from those kinds of demographic inversions. The combination of worsening climate issues with those destabilizations might lead to acute depopulation at the global level, but not likely of a climate-friendly variety.
Destroying the world to improve some portion of the climate experienced by some portion of some population at some unspecified later date a century or more in the future versus, say, geoengineering and attacking the present-day cost structures of nuclear energy strikes me generally as a Bad Plan.
If there are 1 million less children born in the US, it's very likely there will be 1 million more immigrants to take their place, and the places those immigrants come from will have higher birth rates to replace them