Earlier quoted context omitted.
More likely, it will wipe out the subpopulation that don't value children enough to overcome that.
Eh, people with kids are functionally “wiped out” within a few generations too. By the 6th generation of offspring, there is only ~1.56% left of “you”. 200 years is the blink of an eye, historically speaking. If you yearn for legacy.. be a writer, teacher, researcher. Zeno is passing on his thinking some 2400 years after his death.
With 3 kids per generation it's 729 descendants, which is over 11 people!
The future belongs to mormons and muslims.