it fails to account for human greed

You say this as if it's an inate trait of humanity when we lived for literally thousands of years as hunter gatherers without it, in shared communities with shared property.

It's created by environment. Not by nature.

Meet the Hadza. A living demonstration of how different human beings are depending on the system you place them in. When humans have neither competition with one another nor a lack of material abundance they become something quite different.