Greed is not something that has to be "eliminated", it simply needs to stop being the primary trait which entire societies are built on.
First, anyone who refers to Utopia as something that should be wanted doesn't know where the word came from or what that book was about... It very much depicts a not-anarchist, not-communist, slave-holding, patriarchal, [fictional] country.
When someone refers to "everyone sharing" they generally mean within communities, not that your person necessarily meant that. Sharing globally makes no more sense than trading globally, and is wholly unsustainable (for physical goods at least). Inside of communities, the easiest, most peaceful, most life-promoting way of interacting is definitely cooperatively, not competitively.
As long as the majority of humans believe the illusion that they are separate from the rest of humanity & life on earth, systemic violence will be norm. The state, religion, war, debt-based banking, wasteful industrialization, classism, racism, and so much more are all based on this utterly immature (and scientifically false) belief system.
Why do you believe societies are built on greed?
The entirety of Euro-American society is based on greed, getting more for self at the cost of all others, having power over others, being well-known... All things which are actually negative for the human psyche, promote violence, and slow the development of the species.
Why do you believe that?
I observe it
Americans give more to charity than any other society. How is that greed?
Those are humans acting out of a natural desire to help others. Unfortunately, in Euro-American culture, those "charities" are simply multinational corporations who have obtained government-approved "tax-free" status, and siphon all that "charity" to a few individuals.
"The entirety of Euro-American society is based on greed".. Society is the cultural norms, the institutions, the government, not the humans involved. There are many humans living within the sphere of influence of that society who do act for the good of others, but the simple fact is that's not what is most valued & rewarded by the society. When the definition of "success" is fame, fortune, and power, then clearly greed is the underpinning of the society.
I don't think most Americans define success that way. We do aim as high we can, in terms of socioeconomic status. I think it's important to have high aspirations, while staying humble and content. A difficult balance, indeed.
And we definitely respect those who do good. On the flip side, some people only do good to assuage their own egos.