In the contrary. That is what people always did. They are family based. They had a house, which they claimed their own. Tools/equipment to use. If the were farmers the land belonged to those who used it. If the land is big enough, everybody is happy. But people get greedy and start claiming the land as their own. The rest are forced to work for them. That is a result of a lack of law. But the idea of having a public wealth is not alien at all. You say "I belong to a company". The company is something everybody shares. If you tell them "the company belongs to everyone" they would look at you and say "ok, so what?". They don't really care. If you tell them "your house belongs to everyone" they will start punching you. "So the neighbor will be able to come inside? I hate my neighbor". That is usually what people think. They want safety and privacy that is why they want their own property. For most people I don't think the idea is alien. And you have one owner and a lot of workers. So the idea would only be alien to a small percentage. Which would still benefit more than the rest...
Communism is just an idea, it doesn't imply a very specific system. There are hundreds of systems that are based in communism. In any case, there doesn't have to be a label on things.
Most of the resources would be public. Asking people would probably result in "I don't have ten tractors to built your office". If they did, then you could start your own business. But at some degree you would need some public resources if we assume that most resources were public.
Centralization is also a form of coordination. Which is vital for a society. People alone simply don't coordinate that much. The key is not to centralize around people with power, but around laws and systems. I don't want John to be in command for all the wealth. But I would like for laws and agreements to distribute wealth, not the idea if you legally get it, its yous.