I haven't seen anyone say that the end of population growth will stop the growth in climate emissions. I have seen it almost universally said that the growth in people with a certain level of wealth (e.g., enough to buy energy-consuming technology such as refrigerators and cars) does cause climate emissions to grow.
Fair enough, let's say CO2 will not stop immediately after population growth stabilizes, but rather after wealth growth stabilizes. However, population growth is strongly related to low levels of wealth, and vice versa.
Activists often like to point at the high per-capita rate of emissions of people in developed countries, but that ignores that there are far fewer such people and that their birth rates are usually below replacement levels. The climate itself obviously doesn't care about emissions per-capita.
This is also another reason why the crux of the problem is not with developed countries. They have all the wealth to optimize and reduce their emissions, but if the developing world is bound towards a similarly high standard of living, that can't really make much of a difference. If anything, the focus should be on making that development as "clean" as possible, which is not the same problem as reducing emissions at home, except for some technological overlap. Alternatively, developing countries could simply be denied our standard of living through international policy. That, of course, would be an injustice.
> This is also another reason why the crux of the problem is not with developed countries.
By far the most emissions, now and historically, are in developed countries. The cause of our current problems is the failure of developed countries, the US in particular, to act.
> By far the most emissions, now and historically, are in developed countries.
If you want to play the blame game for historical emissions, sure, the developed countries are the biggest culprits. That however has no bearing on future emissions.
No policy of today will undo historical emissions, except maybe a significant sequestration effort, but I don't see any of that in the broader discussion. It's all about how the US needs to reduce current emissions, which would still only amount to 15% of worldwide emissions if eliminated completely.
We also can see that the majority of current emissions are coming out of developing countries, unless for some reason you want to count China into the developed countries.
