It seems like you didn’t finish your response… Why is depopulation terrifying? And why shouldn’t we be concerned about resource constraints? Malthus being wrong implies nothing about the future.
As an anecdata, most people I know are somewhere on the low-class to upper-mid class, and the ones who want kids seem to always have at least one, consequences be damned, and the ones who don't, often don't put a price tag on it and merely use it as an excuse if they feel pressured.
Also the `natural instinct` may not be a given here, since up until recently the instinct to have sex and procreate meant the same results for humans just like other animals, which no longer holds true either.
When we look at actual billionaires, we don't see huge fertility levels. Maybe on average a bit higher than the average couple today, but nothing really significant. It's not like Bill Gates and Warren Buffet have been trying to compete with the Duggars.
The only thing more resources do is allow people to have the number of kids they truly would like to have. Most women really don't want to squeeze 15 kids out of their vaginas, and are generally happy with 2 or maybe 3.
Migration helped to mitigate that. Regarding fertility rates so, the developed West is just ahead of the curve. With economic growth and stability, the rest of the world is following the same curve Europe and the US do for quite a while.
I think, that ultimately, global population will stabilize, including individual countries. There will be dips and spikes, as usual, overall so we should be fine as a species.
How to support the elderly in a world where the same GDP is produced by less and less working age people is a question so: using salaries as a basis for social securoty and public health care won't really work as well anymore. Taxing corporations and wealth (as in really wealthy, being a paper millionaire just because you happen to own a house does not qualify) is one option.