Capitalism doesn't assume anything, it wasn't thought of and created, it arose from the commodification of production and distribution towards the end of feudalism. It arose naturally, without a plan. Communism isn't a "plan" either, Marx analyzed where capitalism was necessarily trending towards and saw that as production was socializing, profits were remaining private, creating sharper contradictions and crisis. Communism socializes the profits of production and distribution, and finishes capitalism's socialization process.

Neither of them are built on any assumptions surrounding greed whatsoever.