I would look at the case like this. Suppose that a strategy game has America represented in it, and to show the importance of fast food there, it has access to the McDonald's building. However, McDonald's is an international corporation, so obviously Canada and France should have it too.
That seems to be the logic behind giving it to every Hellenistic/Hellenic faction. Granted, there are playwrights that are not Athenian. I found browsing Encyclopaedia Britannica's list of Greek playwrights that there is Epicharmus (From Sicily), Alexander Aetolus (Who served in the Ptolemaic court), Herodas (from Cos), Philemon (from Sicily), Sophron of Syracuse, Choerilus (from Samos). The rest are Athenian, making them make up 70% of listed Greek playwrights. I'm sure there were many other writers from other cities, and given the number of Sicilians represented, I would endorse a Sicilian theatre, but the whole notion of extending that to other factions feels a bit strange.