Yes that's true, but it has a lot to do with the greek mentality...
Both Athens and Sparta were Hegemon, all the other members participated in an epimachia (on paper was simply a defensive policy), so their actions were pivotal...
But they didn't held any power from a "constitutional" level, Athens almost by accident ended up having poleis looking out for her and Sparta was held in high esteem for its military fame...
They were acknowledged as Hegemon of the League and that's the power they had over the members, but it wasn't like the other poleis were Athenians themselves or participated in their "state"...
Similarly you don't hear of the League of Corinth marching east to take over Asia and punish the Persians, but again on paper that's what it was...
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