I would disagree that the greed of the Elves was caused by their long lives. Of course the prolonged life compared to Man in fact furthered the grief some certain Elves caused to others and themselves endured. But the reason for this lies not in the nature of immortality; I think this would be a wrong assumption within the cosmology, too.
Such deeds as fueled by the desire for the Silmarils, for example, were just that; and Man proved no more able to resist such cravings than Elves.
As for the other great part, we have the important circumstance of the coming of the Elves to Middle-Earth, even if it originally only means the Noldor:
"And those that endure in Middle-earth and come not to Mandos shall grow weary of the world as with a great burden, and shall wane, and become as shadows of regret before the younger race that cometh after."
As for the others, this unfulfilled longing for the Realm of Bliss may be so deeply rooted in the nature of the Elves that it affects even those who have never been to Valinor at all.
Mith (get well, you hear!) probably summed it up quite well with his provisionarily concise statement of 'mixing cause and effect'.
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