I would phrase that as "having children of their own is goal number one for [all adaptively-fit lifeforms that undergo sexual selection pressure]." The genes of all plants and animals alive today came from the subset of their species that wished to procreate.

Or, to put it another way, among gene sequences that attain fixation through sexual selection pressure, any sequence that impels procreation as a terminal goal is going to be fixated more quickly than any other.