It's already eroded in many countries right? Gendered patronymic names used to be common here in Sweden - Katarina Gustavsdotter (Vasa) was the daughter of Gusav Eriksson (Vasa), who was the son of Erik Johansson (Vasa), &c. - but gendered patronymic names eventually became permanent last names that got inherited over multiple generations.
So now we have a few hundred thousand people with the last name Andersson, despite most of them not being Anders's son.