Constrain your analysis to Hellas and call it bi-polar
The reason that allowed the bi-polarity, is the major cause of the Pelloponesian war.
The reason that allowed multi-polarity, which in turn turned to bi-polarity, is in a nut-shell: The priority of the "city-nation", over the "country-nation".
Use the example of the Corcyreans to buttress this point:
The Corcyreans were a Corinthian colony, just like the people in Epidamnus were a Corinthian colony. The Corcyreans made war to the Epidamnians and when the Corinthians came to their aid, the Corcyreans went to the Athenians!!!
So, we have colonies of Corinth, not simply revolting against the mother and becoming independent, but also attacking her other colonies, and when the worst comes to worst, making alliances with Athens in order to further damage Corinth, and while consciously knowing that after this, there would be no other soltuion, except for destruction of the Mother, or their destruction.
Since you have read Thucidides, you must have observed that the Greek cities were downright pragmatists:
In Book III, The Mytileneans address the Pelloponesians:
'Had all the allies retained their independence,we should have had better assurance that they would leave us as we were; but when the majority had been subjugated by them, they might naturally be expected to take offence at our footing of equality; they would contrast us who alone maintained this equality with the majority who had submitted to them; they would also observe that in proportion as their strength was increasing, our isolation was increasing too. Mutual fear is the only solid basis of alliance; for he who would break faith is deterred from aggression by the consciousness of inferiority. And why were we left independent? Only because they thought that to gain an empire they must use fair words and win their way by policy and not by violence. On the one hand, our position was a witness to their character
Maybe these are a bit more helpful.
"The mutual fear of each city"
Each cared only for his own city and its tributaries. And each care for his own city's reputation.
The Spartans would never allow Athens to grow big enough and take over the leadership of Hellas, why? Because, of the multi-polar identity, and because in this multi-polarity they were deemed the Best, especially after the Persian war and the 300, and all that jazz.
EN EL ED EM ON
...take your common sense with you, and leave your prejudices behind...