I disagree that the population would continuously shrink by half until no one is left.

There is zero reason to think this when the birthrate of most White populations is close to 1, it is already extremely close to dividing in half each generation in all European countries and White America. It's not easy to bring birthrates back to replacement level and has never happened before. If you think you can bring the White population down to 5 million (like the Georgia guide stones) through falling birthrates and then just say have 2 kids each now, then that is stupid and obviously wouldn't work.