"This decreasing relationship between fertility and income is well known to economists and demographers alike. In addition, it holds true over time: Rich countries, such as the U.S., have experienced a remarkable decline in their fertility rate as they became rich. Also, the relationship holds at the individual level, as rich families tend to have fewer children than poor families." from: https://www.stlouisfed.org/on-the-economy/2016/december/link...
The problem is in modern "wealthy" society, everyone is allowed to work (to be clear I'm not saying that's not a problem in itself), and the Red Queen effect means that within a couple of generations¹, most couples are both in full-time work just to afford rent and the "basics" of a modern lifestyle. Children are now a huge opportunity cost, one that might cost you your home. Then, because the couple would have prospects to offer the child, the common human instinct is to invest everything in them or their future, spurred on by the social expectations and the Childhood Industrial Complex. Vitamins and private healthcare into expensive high chairs, a "safe" car and a top-line car seat, toys, computers, clothes, experiences, holidays, housing near good schools, tutoring, a degree etc. Plus the fairly modern sentiment that you should spend as much time as possible with the child, which may inhibit large families even for those who can financially afford them. The expectations around what a "minimally non-negligent parent" must provide children are so high that many people think "I quite literally cannot be sure to provide that, so I should not have children". Of course in the background, "don't have children if you can't afford them" has been the tabloid "anti-scrounger" slogan for at least a generation now, and religious adherence is way down in wealthy societies.
It's a hell of a catch, as Heller would say. Be poor and offer your children almost nothing material in life, and so have them, or be rich and be unable to offer your children far more in an absolute sense than the poor person could, but still far below what you would want to, and so forgo them.
¹ After a couple of generations of taking up the slack in the middle classes (e.g. go-getter Yuppies giving their children unthinkably luxurious childhoods with their new dual incomes, plus the productivity revolution initially paying out as worker wages), the Millennial generation was the first to really notice en masse that they really could not provide to their children what their parents provided to them. Certainly I can't give my children what my parents gave me, and I'm in roughly the same income decile.