We will have to disagree on your premise 'Greed' is only really possible in a society where having plenty is also possible or thinkable." A number of factors can drive greed. A mentality of scarcity can lead to greedy accumulation that deprives others of their needs. A fear of having a lack can cause people to hoard or take from others. A lack of compassion for others also drives greed. None of these factors are necessarily absent when the greed is triggered.
I don't think stabbing someone for the last crumb of bread is "greed" exactly. Anyway I said you would have to imagine that it was possible to have more than someone else, so if it is possible or imaginable to accumulate more, then greed can exist and flourish. In a society where survival is only possible by mutual cooperation where greed means exile, there is effectively no greed, because that will kill you, not advantage you. I do believe there is a a dialectic here, because abundance can produce greed and the idea that you can have and even deserve more than someone else, but the idea of communism is also only possible if you can imagine the same sort of material abundance, where everyone's needs can be met.
They killed 100 million in the 20th Century alone. Shudder to think how many they’d kill if they were better organized.