No, FooHentai is right. We're screwed, Malthus-style, in the long run no matter what we do. The problem is that while modernism does tend to moderate fertility, it doesn't do so across the board. Some subgroups nevertheless have fertility far above replacement, and the exponential growth function tells us that these high-fertility groups will come to dominate the population.
In other words, selection pressure ---biological, cultural, doesn't matter --- always wins in the end. Mother nature has the last laugh.
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?
In other words, selection pressure ---biological, cultural, doesn't matter --- always wins in the end. Mother nature has the last laugh.