Your analysis isn't unsound, I just tend to think capital is less deliberative in it's processes. It also explains why birth rates tend to fall in developed capitalists nations while they continue to grow in periphery regions, it makes sense to just buy cheap labor from an "externalized" source rather than bother to pay for social reproduction/expansion. More importantly it explains the declining birthrate trend in imperial core countries without falling back on fascist Malthusian bullshit that places the onus on individuals and morality.