In preparation for discussing climate change:
There are currently 7.8 billion people on earth. In 1950 there 2.5 billion. At current rates, demographers project the population will stop growing in 2100 at 11 billion or so. It would then take something like seven generations at US population rates to get back to 2.5 billion. That is at least a century, maybe longer with delayed childbirth. I am not sure that we'd be in any way short of people at 2.5 billion, a number seen in the lifetime of still living people and not in any way a dystopia of underpopulation.
Note that one way to reduce the pace of climate change to be generating electricity for fewer people and needing fewer cars. Now let me be clear -- this does not mean I have any patience for coercion in these areas. That way lies madness. But I am not sure that a modest drop in population is the least bit concerning and that we can have a rich and full civilization for the foreseeable future on these trajectories.
And once we move beyond a couple of hundred years, any likely predictions are useless anyway. Imagine trying to imagine 2020 in 1814? Like the whole context of the issues facing world powers and the human race would be sharply and dramatically different.