There are actually a lot of studies of this nature, across Europe, Asia and the Americas. This result is not unique to Florence - you get much the same result everywhere in the world.
Furthermore, this result seems primarily driven by factors intrinsic to the people/families themselves and not to the society they live in. There are a number of invisible subgroups (e.g. "New France", or people with names like Bauchau) which underperform or overperform across the generations. And when people shift from one society to another (e.g. West Bengal to America), the effects persist.
However he’s an economist, not a geneticist. And the description of the book on Amazon focuses on last names and ancestry, not genetics.
https://www.amazon.com/Son-Also-Rises-Surnames-Princeton/dp/...
This book looks to me like it’s arguing that social policies don’t do much to affect familial networks, not that it’s arguing that the elites all have magical genes that keep them on top.