One's memory is better preserved by intellectual feats or architectural monuments. The latter are much better conduits than children and grandchildren. Still, this indoctrinated misconception is so strong that a baby boom characterizes post war periods. Having been existentially threatened, people multiply in the vain belief that they thus best protect their genetic heritage and fixate their memory. Dysfunctional families have more children than any other type of family arrangement.
Children are an abject failure at preserving family cohesiveness.
It would seem that the number of children, or even their very existence, is not correlated to the stability of the family. They are the results of accidents and mishaps, wrong fertility planning, wrong decisions and misguided turns of events. Children are still economic assets in many parts of the world. They plough fields and do menial jobs very effectively. This still does not begin to explain the attachment between parents and their offspring and the grief experienced by parents when children die or are sick.