This is a very bad analogy. Markets behave like an imperfect optimisation algorithm, and you can prove that, under some conditions which are most often met, they give people what they want. In fact, you can almost always expect governments to be less effective and less rational than markets in allocating resources to satisfy the desires of people, even when democratic. You can prove it either by using the same logic that tells you when markets fail (externalities, information asymmetry), or empirically by looking at what was basically the most perfect A/B test we had on society over the 20th century. Although it was a comparison between mixed economies and fully centralised ones, there is no reason to expect the optimum mix of centralisation/distribution to be closer to the worst-performing one (the fully centralised one).