Anyone who looks at a map can tell that Corinth has one of the most strategic locations of any Greek city. Located in a commanding position on the isthmus connecting the Peloponnesian peninsula to the rest of Greece, it had harbors on both the Gulf of Corinth and the Saronic Gulf, offering it an unmatched ability to communicate with any of the seas around Greece without having to round the Peloponnese, while also controlling all land communications between the Peloponnese and the rest of the world. Thanks to this position, the city was incredibly wealthy and had trade connections across the Greek world. Moreover, it had a large network of colonies, including wealthy and developed locations like Syracuse, Corcyra, and Epidamnus around the Ionian Sea and Magna Graecia.
Yet it never seemed to play the role in Greek politics this geography and these connections destined for it. Instead of being the great competitor to Athens at sea, or Sparta or Thebes on land, it always seemed to play a subordinate role in the classical era of Greek politics. Conflict between Corinth and Athens concerning Corcyra and Epidamnus was the nominal cause of the Peloponnesian War, yet that war is widely and correctly considered a conflict between Athens and Sparta, with Corinth just another Spartan ally. They played a more important role in the Corinthian War, but were still only part of a larger alliance, and that mostly a Persian proxy against Sparta. Afterwards, like the rest of Greece, they slipped into being subordinate to the Macedonians and, later, Romans.
So, why wasn't Corinth one of the big players in classical Greek politics, the way that Athens, Thebes, and Sparta were? Why don't we hear about a Corinthian League aligned against Athens, or a Corinthian Empire against Sparta? What kind of changes would be necessary to make Corinth spoken of in the same breath as those other cities?