Birthrate declines as a society becomes more prosperous and women gain control over their reproductive rights.
In fact, the correlation is the opposite of what you said; wealthier people have fewer kids than poor people in almost every country. Your suggestion that people decide not to have kids because they can't afford them is not supported by the data; those who can most afford the kids have the fewest.
https://www.statista.com/statistics/241530/birth-rate-by-fam...
> Most billionaires have three or more children, the GoCompare analysis found. Among them, 5% had no children, 9% had one child, 23% had two children, 25% had three children, 17% had four children and 21% had five or more. Amazon CEO and founder Jeff Bezos has four children, and Bernard Arnault, the chairman and CEO of the luxury goods empire LVMH, has five. [1]
So if you're a billionaire, you're having lots of kids, but if you're making 200k/yr you're having fewer kids. It makes sense to me.
[1]https://finance.yahoo.com/news/weird-things-top-billionaires...