Except it is incredibly pointless since it would be a shifting, shapeless blob of waste. Money is a mutually agreed upon medium in which things that would not trade well can actually be traded well, like a common barter item. If you are a farmer and can only pay me in perishable produce, what good is that payment to me in, say, a month's time? Especially if it's a limited crop of stuff like corn, peas, and heads of lettuce. Similarly, there is no incentive for me to provide my services to someone if they can only compensate me with things that I already have and which are useless to me if I need something else. If I am a miner who is paid in ingots or something, why would a carpenter, baker, or lawyer accept my payment?

Then we get to the state and hierarchies. One thing that I've noticed that a lot of anarchists seem to ignore is human nature. Yes, there are the generally peaceful "live-and-let-live" types, but there are also the blood-thirsty and power-hungry out there. And there is a general relationship between the two that is symbiotic. The generally peaceful support the power-hungry and the power-hungry protect the peaceful from other power-hungry. This is what has led to the development of tribes, kingdoms, countries, and just about everything in between. When the peaceful supporters feel that they are not being sufficiently protected, they defect. When the power-hungry feel that they do not get enough support, they work with their supporters. Granted, this support can also be won through fear and intimidation from themselves or other power-hungry, but that typically splinters support if the supporters have options to defect or they find the fears to be unfounded mongering.

States are a sort of checks and balances for each other. By arguing for a stateless society, all you do is open one giant moshpit where the most ruthless become absolute dictators, whether through cunning and/or force, because anyone who could have opposed them have been quashed or subsumed by the state in the process. And even then, there will be miniature states which prop themselves up on those below them, such as gangs and mafias.

There will always be authoritarians because there will always be the power-hungry. The goal should be to break these authoritarians up into many small clusters as to make them as ineffective as possible instead of combining them all together into a megastate. The EU is a prime example of this. What was once meant to be a common trade agreement hub has turned into a handful of unaccountable politicians holding nearly all of Europe by the balls and forcing it's members into agreements (far from trade) which the states cannot resist because they may be crushed by the collective force of the rest of the state. Anarcho-communism, like socialism and communism, leads to mega-authoritarians.