Most the statistics cut off at ~200-300+k income catch all bucket which drowns out the rich averages. See my source above capturing higher income buckets which pronounce the U.
Near equal (higher) fertility at both extremes might be, but not proof of, the hypothesis the dirt poor and filthy rich are the fertility rate you get when opportunity cost looks near 0.
A bucket you often see stopping at 300+k imo far too low as the lower band of that is usually high stress highly educated long hours professional and small biz owners who have insane opportunity cost to have children.