In actual fact , if we introduce women to the idea that they can use contraceptives, and limit the size of their families as a result - like we did in bBritain in about 1950 - they often did.

of course, alongside the family planning goes putting the kids in schools, better health care so more kids survive, etc.
once kids are seen as economic liabilities instead of cheap labour, parents have fewer of them. populations go down take a look at the UK, most of europe in fact ...