Here's a thought experiment:
Imagine trying to operate a modern county hospital as an anarchist organization. For the sake of the experiment, let's assume this is a miraculous money-free post-scarcity society and we're not worried about the cost associated with anything or handling billing nonsense. We are absolving ourselves of all of the complexities of the accounting department, thus simplifying everything. Materials and labor are supplied for free, somehow (handwaving details TK).
OK, so what we're concerned with is system management. Inputs and outputs, and internal processes. Patient appointments, work shifts, task assignments, surgery schedules, emergency response, education and training programs, laboratory analysis, medication distribution, food distribution, waste disposal, supply requisition, shipping and receiving, inpatient and outpatient care, and above all sanitation for everything. The goal is to have the right resources in the right places at the right times. If you miss the goal, people die.
Is this a system that can operate effectively without dedicated authority figures? without centralized management? Can a hospital be run effectively as a coalition of equals, with no empowered oversight?
No.
Why would the rest of a society that exists around a hospital be any less complex in practice?