Empirically, seeing that couples in general find child rearing too burdensome to maintain replacement rate, it seems that the current split is not the correct one.
That there are willing young immigrants available is a historical accident. As countries develop economically their birth rates consistently drop, eventually to below the replacement rate, as can be seen in almost all first world countries. Taking first world countries as a closed system my argument applies. Allowing for immigration means the system now depends on a pool of readily available people who live in economic misery to supplement the first world population, which is not a particularly ethical arrangement.