Really with only 1 child for couple the population doesn't simply stop growing, but decreases...I guess it's a matter of limiting the poor ones to 1 child in order to allow the "elite" couples all the children they want.
Anyway your worries are spot off, apart those crazy Chinese no one really wants children , they are just the unwanted side effect of sex, so the progressive spreading of condom use will wipe off the population in the end ... it's a matter of three/four centuries at most.