I think the latter Chinese policy in particular wasn't too restrictive and 2 children were a large enough limit to not skew numbers too much. That policy didn't push people from stopping to want those 2 children. Their previous policy worked much better.

If I wanted to stop people from having children I would promote hookup culture, feminism and economically reward unstable families. A touch of propaganda on how scary and life ruining it is to have a baby and in a couple of generations the birth rate should drop below replacement rate.