Most people think that without the current situation of society plaguing us, the world will generally be a better place. However personally I will dismiss that as naive thinking.
People are born with strong survival instincts. As Steve Jobs said "everybody wants to go to heaven but no one wants to die to get there". Survival has always been a game where the fittest are the ones on top and most likely - alive. Without the global currency of money DOESN'T remove greed. Greed is a temptation and instinct of survival. If we don't fight for money, we fight for other things. Everything in this world is of limited supply including sunlight, where the sun is believed to be a star and would one day die out too.
Religion to me is pretty similar to law. Where they preach for you to do good or risk being punished and sent to the depths of hell. Without law and religion, people would likely to be free to do whatever they want whenever they want. What kind of world would that exactly be is as good as anyone's guess but I can foresee it being a very very chaotic situation where people run amok. Many people are conforming to societal requirements because they are afraid of the consequences of breaking the law or doing something immoral. When such psychological restriction is removed there is no limiting to what all people could end up doing.
Instead of the world that many imagine would be freed from the sufferings of civilization may end up bringing the bloodshed of barbarism.