why do the olympians constantly move to the place where the spirit of western civilization burns brightest

I think the Gods are always closest to the fire,

Come now, Percy. What you call Western Civilization... is a living force, collective consciousness that has burned bright for thousands of years. The gods are part of it, [a] fire started in Greece. The heart of the fire moved to Rome, and so did the gods... wherever the flame was brightest, the gods were there. They are now in your United States. Look at your symbol, the eagle of Zeus. Look at the statue of Prometheus in Rockfeller Center... like it or not—America is now the heart of the flame. It is the great power of the west. And so Olympus is here.