Yes it self corrects if left alone. I have a theory that population was made to explode artificially. The obvious example is Africa where the west stepped in to avert famine but from that point on used it as a dumping ground for agricultural surpluses, making them dependent and removing the impetus to innovate and adapt. Their population exploded from the mid 80's, before that it was quite small.

But more generally I assumed they wanted a global increase to 1. make money from larger markets, 2. create a need for eugenic programmes directed artificially by them (mass sterilisation by transmissible disease created by them or perhaps that was the covax). 3. have a large population necessitating "global solutions" that they direct

Eventually there will be a correction whether directed by them or as a result of a general collapse of the support systems they built (if they are in control then the wisdom of the following epoch will be "don't let population get out of control again" which will mean breeding licences