I think that historically big powers in Greece relied upon several strategies to maintain their own hegemony:
Become very rich, acquire prestige (for example for contributions to the wars against Persia) and make alliances with people, ensuring their continued friendship with either bribery or the looming threat of a "league action" against recalcitrant allies.
Greek politics was odd and probably isn't well-represented in the game, which uses more modern assumptions about conquest. I can't think of too many examples where Greek states actually invaded and conquered their enemies' towns. The usual practice in war was to raze the walls, execute part of the population and install a "friendly" tyrant or ruling council. Places were unlikely to be occupied (at least not for long), even less become, for example, "culturally Athenian" (in game terms, being able to recruit home troops from). Factions with a small "cultural" base do seem to be at a disadvantage because of this, and I do think the cultural system is quite flawed. Such a vast area of the Aegean did not feel such close ties with Athens, but because of the way the game works, it has to be represented that way.
I do think that there was a distinction between language groups in Greece though. I'm struggling to remember but there were at least three major language families: Doric, Ionic and North-Western Greek. The Athenians, who spoke Attic Greek, were a part of the Ionic language group. Perhaps not coincidentally, most of Athens' allies were also Ionic-speaking. A way this could be represented in-game, and make things easier for smaller factions, is as follows:
1. All factions and cities are assigned a broad cultural group: Doric, Ionic, NW-Greek etc.
2. If you conquer a city with the same cultural group as your faction, you can recruit allied troops from it.
3. If you conquer a city with a different cultural group then you're stuck with mercenary units.
This would encourage a more historical play-style, with Athens finding it easier to conquer the islands of the Aegean and the coast of Asia Minor, and Sparta finding it easier to dominate the Peloponnese (though strictly speaking there were various language groups in that area).