I don't know if that works for reducing your carbon footprint. Children don't add to your personal carbon footprint. They're individuals on their own.

You'd never consider yourself to be part of your parents carbon footprint, in need of "reduction", would you?

In a global sense, sure less population means less carbon footprint, but that isn't the end-goal of civilization. To me, the end goal of civilization is life---human life in all its myriad ways, and to its utmost fulfilment. An earth without humans is a poorer earth.