I don't think the way the issue is currently framed is concerned about long-term extinction. All of the low-birthrate articles I read are from the POV of "how do we artificially prop up birth-rates to continue the infinite growth economy". The current "function" is built around optimizing on the wrong parameter. Structure your economy and society around human fulfillment, not infinite growth, and people will be more inclined to reproduce. This is never a point of discussion though because it goes against corporate interests.
Young people grow, old people stop growing. To keep the economy growing, you need to keep the population young i.e. maintain a fixed young to old ratio.
If the young to old ratio drops, then the economy won't grow and there is absolutely nothing wrong with that. All you need is an economic model that doesn't depend on economic growth as a bandaid for social problems.
Even more you need population that is "middle" aged. Old enough to work, not too old to be outside working age. Both children/teens and pensioners need to be supported by those working.
