The point I'm making is independent of whatever trap you're trying to set --- the specific groups don't matter. As long as some group has high fertility and is able to pass on this high fertility to future generations, the dynamic I'm describing applies.
Your reasoning just reminded me of that of some confused individuals that see everything in purely biological terms. Fertility alone isn’t some silver bullet for the success of a population, even for bacteria and ever more so for people. Why isn’t there already a dominant Uber-fertile group?