Doesn't the very word barbarian mean they are not from a city?
The original ancient meaning of barbarian was anybody not from Greece or Egypt. So yes, people from the developed cities of Persia or North Africa were all barbarians. It wasn�t just tribal peoples from Germania and Gaul.
The modern meaning of barbarian is somebody who acts cruel and brutish, and has nothing to do with being tribal or indigenous. The derogatory term for tribal peoples in the colonial era was usually savage. While they might also be called barbaric, this term wasn�t used exclusively for tribal peoples.
Also, there is no reason a street urchin could be a wizard, but DnD allows it. It�s fine.
This thread and your objections are all ridiculous.