When you think about it, all creatures on the planet have to "work" to survive. Predators have to hunt, plant eaters have to migrate and browse constantly. Many animals need to dig or build shelters. This would have been true for early humans, who probably lived in small family groups. Humans have four basic needs: food, shelter, a means to compensate for our lack of a thick haircoat, and a reliable means to procreate.
As is true in primitive societies even in our own time, humans tend to divide labor. Even with early humans, some would hunt. Some would gather. Some would be responsible for finding and tending the shelter. As humans began to wear clothes, some would be responsible for preparing the skins and plant material used for clothing. Eventually customs arose around the need to procreate, and the beginnings of what we know as marriage appeared.
Particularly in early humans, the survival of the entire group depended on the skills of the best hunter and the best gatherer. It is likely that they were given (or took) the choicest food, warmest clothing, best sleeping areas, and most desirable mates. As humans began to use tools, and as societal groups grew larger, the concept of private vs. communal property took hold. The best hunter/gatherers evolved into tribal chiefs who were still able to claim the best food, goods, services and mates the tribe produced. In time, barter between tribes developed, then early forms of money. In time, chiefs became kings, and kings gave way to dictators and presidents.
The point, of course, is that even as human society evolved from small family units, to tribes, to villlages, towns, cities, states, and multi-state nations, we still operate on a survival imperative. So your question really probes whether or not we can return to the earliest form of human organization: communal living in which resources are developed, processed, and shared equitably by and for the group; a time when there was no private property. The answer is: It is possible for communal living to work successfully in small groups. But, as the experiences with communal living at the nation-state level around the world has shown, it's nearly impossible for the huge impersonal societies we call nations to do.
One might argue that communism has had a measure of success only in Red China, an ancient society that was accustomed to centralized control 2000 years ago. But it has failed miserably everywhere else, and even in China goods and services are not distributed equitably. Their society has rich and poor, upper class and low, just like every other nation. The reasons communal nations fail are several and complex, but I suspect at bottom it's because: (1) someone still has to produce food, goods, and services, (2) ensuring a truly equitable sharing of both production and resources is impossible, and (3) the best producers and natural leaders among us will always claim or seek to claim a greater share of the communal wealth — which loops back to the impossibility of ensuring truly equitable sharing of production and resources.
someone still has to produce food, goods, and services
What if those doing the work are robots?