Back in the 90s, there was fear about a population bomb. 10 billion people by 2010, mass starvation, etc. We've successfully defused the population bomb since, and now the conversation has flipped. In most developed countries, there's declining birthrates and new concerns over who will support the future economy. The problem now is that these countries do very little to support new families and children. Housing is expensive, childcare costs are crushing, expectations on parents is higher than ever, and there's less community support than ever before. So it's really no wonder why people are choosing to have smaller families or no kids at all.
No; we just have birth control that works. The rest of these are all parts of the puzzle that help people not desire having offspring, but previously there simply wasn't a 99% fool-proof method to do so aside from abstinence or hysterectomy. So; regardless of economic factors, people had kids and dealt with those outcomes.
Is this true for very wealthy people, or only for above average earners?
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."
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.