You're right that a communist society could not function with the type of mindset the average person in our capitalist culture has. Changing that mindset is one of the principal challenges of the revolution. Nevertheless, the idea that humans are naturally greedy is a myth that happens to flourish because we live in a society that glorifies consumerism and gaining wealth (the so-called "American Dream" which is just that, a dream). People have been culturally indoctrinated into the idea that having more money and more stuff is not only great, but perhaps the main goal in life.

This all needs to change. But cultures change, societies change, ideas change, economies change. Communists are just trying to map out what direction we should be changing in. We want a society where wealth isn't concentrated into the hands of an elite few, where children don't have to grow up starving and homeless because their parents are poor, where workplaces can be controlled democratically instead of in totalitarian top-down hierarchies, and where the idea of a successful life isn't owning the best shit on the block but rather real meaningful activity.