[thaumasiotes]

> It's sensible to expect that families with that kind of wealth to leave a trace in their ancestry.

The ancient patrician families had trouble with going extinct. Their decline started long before the imperial period.

Later European kings had the same problem, sometimes just failing to produce any heir. It only takes a single generation and the family is gone.

If anything, I'd attribute family extinctions like this to monogamy. The two standard defenses against a failure of this type are (1) letting a man marry into the family by wedding a family daughter (as opposed to having the daughter marry out into the man's family); and (2) taking more than one wife, which offers dramatically greater opportunity to reproduce.