Mravac Kid 说:
If you want to go that way, better to give the smith some sort of bonus for his culture-related items... everyone decent enough can make decent enough armor/weapons of any type (it's not like they're greatly different technologically or something, it's all the same basic principles), but is better at doing his specific stuff. Maybe limit their ability regarding making masterwork stuff from other cultures.
Actually, they ARE greatly different technologically. These different technologies are driven both by raw materials available (even something we think simple, like iron, varies by region), and the culturally-driven intended use of the piece of equipment. The ancient and medieval worlds were places where mastery of a task was a matter of rote learning with the materials to hand, and becoming a master of making one type of steel into a broadsword in no way means one can make a different type of steel into a sabre. Becoming a generalist was a thing for the future, hence the term "renaissance man".