> Natural selection will make that desire stronger over time.
Natural selection doesn't work like that.
There is no guarantee that traits appear because they are needed ; only that traits that somehow appear may spread if they are useful or associated with something else that is useful.
But don't we have that trait already in some form? Some people want kids, others don't. The traits that make a person more likely to want kids will become more common.
If we don't have such a trait and the decision to have kids is based entirely on the environment, then this evolution will be cultural instead of biological. Cultures that have more kids will replace those that don't.
My point is more theoretic that an actual reflection on what will actually happen, because I'm not better than the next person at predictions. Simply put: just because a species needs to change in order to adapt, doesn't mean they do. Geologic strata are littered with species that no longer exists.
As for culture, it is not a static thing, or indissociable from individuals. My grandmothers had 6 and 8 kids, most of my cousins have 0-2 kids. So considering my grandmothers' behaviour and my cousins', Are they from the same culture? Will people that reproduce more today convince their children to do the same?
In either analysis, it's really hard to use natural selection as a predictive tool.
We, or at least some of us, most definitely have such traits.
Holding newborn babies tend to have a quite obvious and equally instant hormonal effect on a lot of people. For some people, even a few such encounters may be enough to induce baby fever.
And there are other factors at play, too, that are also inheritable. Factors like impulse control, introversion / shyness, ambitiousness drive and tendency to magical /religious thinking may all affect the number of offspring one way or the other.
So all that is needed is a few generation of strong selection pressure for such traits, and we're back to overpopulation again being a much bigger threat than population collapse.
Natural selection doesn't work like that.
There is no guarantee that traits appear because they are needed ; only that traits that somehow appear may spread if they are useful or associated with something else that is useful.