Is it a flaw to desire more than we have at a given time? That sounds to me like "savings" in an effort to guard against future uncertainty.

I think you're right though that greed has religious roots. That hypothesis also dovetails with what I'm saying: If you properly trust in and have faith in your god, you wouldn't stack more than you need in the moment. Since god will act as insurance against uncertainty, you don't need to save overmuch.

The "greedy" are those with the least faith.

Well yea, count me among that lot, lol :D