A scenario of woman chasing men for $

As a fiction writer, I think up odd scenarios. It has struck me that
there is an instance in which it makes sense for the woman to sexually
pursue the man. A woman is poor. A man is wealthy. She deliberately
gets pregnant by him. After that, she's the only one with any choices
so she has the baby and sues the billionaire for child support. Since
he's a billionaire, the court orders a big child support monthly
payment. Thus, Mother can ride the gravy train for 18 years.

I don't know that anyone has ever done this but it seems to me that it
could be done.