Paying your enemies to fight each other is a lot cheaper than fighting them yourself

Explanation: While in popular history, the Greco-Persian Wars are emphasized as an attack by a foreign power which united disparate, quarrelsome city-states in defense of their common liberty, the truth is more complex.

First, that Persia always had allied Greek city-states which sided with it, giving them an arguable case for ‘liberating’ rather than ‘conquering’ Greece. They are, after all, only acting in favor of their allies, who are themselves native Greeks!

Second, that the hegemony of powerful Greek city-states over smaller city-states was often so severe that many considered Persian hegemony to be better - or at least no worse - than hegemony by a fellow Greek city-state. Speaking of ‘liberty’ for Greece is all very well and good, but even if you exclude unfree populations like slaves, clearly not every polity is getting an equal share of this ‘common’ liberty.

Third, after getting their nose bloodied in open warfare and having a rather large empire of other concerns to attend to, Persia largely opted to fund the internecine wars of Greek city-states against each other, especially the ever-burning rivalry between Athens and Sparta. Despite the lionization of Sparta and Athens, neither city-state was too proud to take an alliance with Persia against against their fellow Greeks.