Look around you. Under what you just proposed, they decide what to produce. What you will see is a lot of people starving, because most undesirable activities that are essential to modern urban living will go unattended. By the way, you cannot have an anarchist structure trying to co-exist along side a central government structure. Eventually, the central government will overwhelm the anarchist, especially the first time something goes wrong
You would need essentially a religious like structure to either persuade or psychologically force people to buy into that