I think a similar argument can be made for the legacy of the indo europeans. You just have to go a bit further back, before greek and hittite and celt and iranian/aryan and vedic cultures where a distinct thing, there was one single culture speaking a single language: the proto indo european people and culture. They had a lot of success (horse drawn carts with wheels, bronze working). They slowly spread east and west and slowly diverged for several millenia until we reach the time frame you were talking about. Those descendent cultures didn't branch and stay isolated forever after; as you correctly point out, they did influence one another again and again in successive waves.
The original question in this thread was: why was PIE culture so successful that it supplanted almost all existing PRE-indo-eurpean languages. Vascon and Etruscan survived (and possibly others), the former evolving into modern Basque, and Etruscan slowly dying out (very likely by the end of first century AD there were no more etruscan speakers)