The Panhellenic Sanctuary sites

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The Panhellenic Sanctuary sites, like Olympia and Delphi, are very “Greek”. That is, although there is no
single country that is Greece, these sites unite all Greek-people with a shared sense of Greek identity, in
the worship of their Greek gods, celebration through Greek ritual, and giving of Greek-style votives and art.
So why would Lydian King Croesus, or Pharaoh Amasis of Egypt, for example, get involved? What does it
mean for non-Greeks to participate in Panhellenic Sanctuaries? Why do you think the foreigners (who by
the way the Greeks all called “Barbarians”, from the sound a dog makes, barking: “bar-bar”!) would be
interested in Greek cults? What would they gain by participating in them?
Short essay, informal answer is fine if it addresses the question seriously. Cite everything you use.