Maybe that is what will happen, at least in the medium term (100 years or so). History is the record of the expansion and contraction of different populations. The defeat of a state with a falling population by one with an increasing population is a major feature.
Keep an eye on what happens with China and Russia in the next 20 years.
On the other hand, the United States and Western/Central Europe once had healthy birthrates, without being significantly "repressive." There are many factors.
Compared to today women in American history had far fewer choices and were much more repressed. Western Europe was dominated by the Catholic church far more repressive at that time than now.