Yet, richer people have fewer children. It isn't clear that reducing costs (making people richer) would actually increase birth rates
There are many examples of very wealthy people having lots of children. Children are still a significant investment for high earners, but at a certain wealth level it becomes inconsequential.
Quick google shows some support for this idea:
"There is a new emerging trend where better-off men and women are more likely to have children than less well-off men and women."
https://ifstudies.org/blog/more-babies-for-the-rich-the-rela...
ergo, there is probably a level of financial support/wealth at which people start having more children. Or more simply, the point at which the personal benefits outweigh the personal costs.
Yes, people are having kids at older ages.
Looking at an arbitrary subset consisting of a younger population when considering lifetime fertility is not proper analysis.