Why do you think that this is true? Look at the countries by hours worked: https://en.wikipedia.org/wiki/List_of_countries_by_average_a... and there is basically no correlation between birth rates and hours worked. Countries with higher hours worked actually have higher birth rates!

[South Korea has a high birth rate for religious groups than non-religious](https://www.demographic-research.org/volumes/vol44/23/44-23....) no religion, 1.13; Buddhist, 1.33; Catholic, 1.16; Protestant, 1.28; and “other religion,” 1.20. This is the same country with the same problems for all groups.