There seems to be some misunderstanding of what communism inherently is and the cultures who have lived in a true communal society. Before modern civilization there were two majority human groups. We'll call them farmers and hunter gatherers.
The farming ethos that came to be was about ownership at its base. In the beginning the ownership would have been a communal land ownership, then of course came the advent of personal land ownership, currency, human ownership, male ownership of women etc etc. But before all that, there were communities of human beings who did not have any of this. No concept of currency, no concept of personal legal ownership of land, ownership of women.
Hunter gatherer communities were genuinely communist communities. Land, the Earth, was a birthright of those born on it. Nobody owned the plot of land where a mother gave birth and nobody laid claim to it. Earth was Earth, and Earthlings belonged to the Earth. Both men and women gathered or hunted food in small groups and any findings were shared among the group. Childcare was undertaken by the entire group, as was hunting.
To put this in perspective, in our society, we are born into a world where we may very well have right to nothing because perhaps our parents own nothing, and since ownership is in many ways a foundation of our social system, where chaste and social rank are very evident, to not own anything is to have no birthright. Now, this in itself demeans us as a species. We are born into the capitalist world and nothing is our birthright. We must always ask permission, work for currency, pay to those who would take our earnings and distribute our wealth to those whom we do not even know.
We are given little and so we desire to give little.
In almost all practical respects, we are either domineering or oppressed - sometimes both. Those above us own more power, thus are a higher social rank. Those below us own less power, thus are a lesser social rank.
Communism entails none of this. No currency. No ownership. No hierarchy. Humans are given to from birth, and will give back when they are of age. Each man is alike to another. The bonds of society are founded on the mutual benefit of an egalitarian equality. Respect demands a man to eat his share and no more. The attitude to share creates an atmosphere of community. Yet in our current society we are taught 'earn, have, take' and this creates huge gulfs in social rank. We have a hierarchy system more suited to some of the ape species than to human beings and the communist ideal is to take that away - to remove rank, chaste, personal ownership and capitalist ethos.
The issue is that we now have a global community of currency based livelihood and so transforming the ideals of the hunter gatherer community into modern terms is incredibly difficult and complex, mostly because of purchase power being currency. Marx wrote in his manifesto that this was the biggest obstacle to a communist society - the dictation of what is purchasing power and how much value it holds. The manifesto starts with a definition of purchase power and Marx examines at length what it inherently means and how it is deduced.
Whoever said human greed is an issue in communist ideology is spot on. The very people whose power it was to dictate the terms of purchase power are those same people whose motives for creating the banking-currency system were little more than greed.
The farmer mentality led to the capitalist systems we now have, and the capitalist ideology is 'more'. It compounds and exacerbates human greed rather than do anything to dispel it. Even some of your ideals of what communism is are from such a starkly capitalist viewpoint that explaining the communist society is almost impossible to do. When someone says something along the lines of 'they'll take our money and give it to the poor and that's criminal' it shows the degree to which the capitalist currency model is embedded in peoples' minds.
Truly communist society doesn't have currency at all.