the reality of achaemenid rule was very light. Alexander was from the part of the greek world that acquiesced to achamenid tribute. Had Darius or Xerxes crushed the barbarians and emplaced some loyalists it would basically just prevent the peloppenesian war which is only important to "le western civilization" creeps in the first place. maybe more focus would be on the west as the italiotes became the standard bearers for 'free greece', probably just in historiography tho unless a spike in immigration made them more able to resist Carthage and Italians.

in any case a triumph over the poor greek savages doesn't seem like something that would rejuvenate the empire, as it became vulnerable and retracted from its furthest commitments there's no reason for its terminal fate not to be sealed from the west anyway. perhaps by the exact same historical personages. overall it's a pretty lame divergence point, California girls of the 30s clearly knew their althistory and recognized when they rely on racist 'clash-of-civilizations' tropes.