The other problem is the prisoners dilemma: if the west stops having children and not-the-west does not stop then within a short time we will have replaced the west with an equivalent population breeding much faster for cultural or religious reasons.

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.