The story of South Korea attempting to reverse the culture of abortion and contraception is not unique. The same problem exists in Japan, China (particularly Shanghai), Germany, France, and other countries. Note that it isn't only that this generation is refusing to propagate life to the next generation. In many countries today, despite the wealth and relatively higher levels of comfort and safety, people are also giving up on their own lives. Not only is depression and suicide more common, there's the push for euthanasia, and many voices for the termination of the ill, the handicapped, etc.
It isn't something that incentives can help with. The soul, in this case, has been corrupted. The solution lies in cleansing the soul. But what is a government to do when they no longer believe in that?