Not surprisingly, the qz.com article distorts the meaning of the original paper and looking at the comments, they seem to follow the false, but suggested interpretation of the paper that qz gives. It's useful to note the title of the paper: What’s your (sur)name? Intergenerational mobility over six centuries. This paper is not tracking wealth, it's tracking income via tax records. It notes things like people who are…
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.