I recently had this thought and I'm wondering if any experts in biology/genetics can chime in and help me. Yes it seems to me that this will be a problem faced

I recently had this thought and I'm wondering if any experts in biology/genetics can chime in and help me. Yes it seems to me that this will be a problem faced by the developed world for the short-medium term future. But does evolution also play a role here as well? By creating a shrinking population, does that not sort of "select" for people with a natural inclination to have more children? How strongly is the desire to have more children tied to genetics? I can imagine this problem solving itself on some timeline if that is the case e.g. people with a strong desire to have children have more kids, their genes are more prevalent while people inclined to have fewer kids sort of select themselves out of the gene pool by having 1 or 0 kids. This seems to me entirely possible, as I know genes can code for basically any arbitrary behavior, but I'm not an expert.