I believe your interpretation of "Valar Dohaeris" is incorrect. This greeting/response belongs to a culture that worships the many-faced god, i.e. the god of death.
My assumption is that "all men must serve" does not refer to performing one's role in the world; rather, it refers to death as an inevitable act of service to the many-faced god.
The address "Valar Morghulis" and response "Valar Dohaeris" are simultaneously a greeting and a religious ritual.