By that logic the richest people should have the most kids. Other than Elon Musk does that correlate at all? The stereotype seems to be the rich city people have less kids and the poor country folk have more.

It's more than just one thing. A lot of rich people value their career highly and wouldn't want to sacrifice the time for kids.

That said, the correlation within developed countries between income and how many kids you have varies IIRC, some places richer people have more kids, in other places they have fewer.

That's just stereotypes. Globally, wealth is inverse with fertility. But within a given country, it's J-shaped: wealthier people have more children on the margin.

Also wanna point out: as you get richer, the social expectations for how you raise your kids get higher in terms of $$$, too. Go upper class and suddenly you need to get your kids into fancy private schools, you need to send them to get horse riding lessons, you need to go on nice vacations overseas, etc.

Obviously these are not true needs, but if people feel like they're needs, they can still become factors in how many kids you have.