Why were the classical greek poleis worse at maintaining balance-of-power than early modern European states? Eventually the hegemon would find itself on the wrong side of a coalition of city states but Athens and Sparta both managed to alternately subjugate a lot of smaller poleis before that happened. Metternich would never have let that happen.
Interesting question!, albeit one I feel unqualified to answer on both sides. To take a stab at it off the top of my head, I would point to three most important factors: geography, the relative preeminence of the various contending city-states, and Persia.
Geographically, the features that led the Hellenic world to be divided into hundreds of mostly small city-states in the first place did not change once a few major poleis had risen to prominence by the early Classical period. Like, Sparta controlled the largest territory of any of them, and their direct control was only ever just "part of the Peloponnese". Corinth had a strategic location, Athens had the largest economy and maritime presence, Thebes had the best gays... You can see why these were the preeminent cities but you can also see why none of them were ever powerful enough to force the other cities into anything other than loosely subjugated alliance networks. That's pretty different from the great powers of Europe, who had deeper internal resources to draw on and were less dependent on a host of lesser powers for their power. The poleis were more vulnerable because it was much easier for rival cities to collapse their fragile webs of control. That vulnerability also made it harder for peaceful coexistence, since any rival could easily nucleate a coalition against you.
On top of this, the Classical Greeks were also next door neighbors with the largest state in history to date. And once the Persians had decided that conquering Greece wasn't worth the trouble, they were more than ready to play the different cities against each other. The Spartans took Persian gold to build a fleet to smash Athenian naval supremacy to win the Peloponnesian War, but they wouldn't be the last.
So the failure of the city-states to stably balance each other was always the likeliest outcome. None of them were *that* powerful relative to the Greek world as a whole (maybe if Syracuse wasn't halfway across the Mediterranean...?), and so all of them could only ever manage to build fragile power bases, which were repeatedly vulnerable to rival coalitions backed by an outside superpower.
That said, your question is clearly implying "did the Greeks just suck at statecraft" and it's hard to deny that they kinda did. Athens was profoundly stupid in how they handled their empire. Use a light touch! Be the stationary bandit! The speed with which the Athenians built a petty protection racket to gild the Parthenon is just deeply depressing. Maybe some of that is just the natural self-interest of a pre-modern democracy, but I'd also point to ideology and statecraft.
Ideologically, there just wasn't enough of a pan-Hellenic sentiment at the time to counterbalance the deep attachment people had to their cities. That simply was the natural unit for everyone to think of. City-states had been warring with each other and exploiting each other since before the return of literacy to Greece, and in a sense the Athenian Empire was just a turbocharged version of that. What are we gonna do, not rip off these other cities that are now in our power? Unthinkable. There was *just* enough fellow feeling to barely pull off victories in the Persian Wars but that was a massive existential crisis and it was still a very near run thing both internally and externally.
In terms of statecraft, we do see further "technological" development as we move from the Classical to the Hellenistic periods. The post-Alexander kingdoms were way closer, and more involved in internal Greek politics than the Persians had ever been. A much bigger threat in other words. And in response to that pressure, we do see the city-states gradually forming themselves into proper confederations, most notably the Achaean League, which covered most of the Peloponnese. These weren't just reruns of the Athenian Empire with a single hegemon, they were actual confederations (although they weren't above forcing cities in to their leagues at swordpoint). They were imo a genuine development in terms of both ideology and political organization, but much too late in history and so of course they got smashed by Rome. Sorry guys, shoulda done it in 480, your achievements would've been legendary instead of "trivia for people who read Plutarch".
Of course a stable pan-Hellenic confederation wouldn't have exactly been the "balance of power" you refer to - that specific geopolitical setup was probably always out of reach. But with a different mindset they could've come up with something stable, perhaps.
