Sometimes rich people do come from poverty. Sometimes middle class people come from poverty and rich people come from the middle class. And sometimes rich heirs and heiresses go bankrupt and fade into obscurity. Why does this happen? Because the people who improve their position are either intelligent or diligent and the people who decline in position are either stupid or lazy.

To whatever degree these traits are genetic, you’d expect them to get roughly sorted out to the point where social mobility would decline, but it wouldn’t disappear entirely.