Neoclassical economics doesn't say what you think it does
The basic reasoning that people tend to use to support the idea that central planning is bad is that in private markets, competition will cause innovation, price-cutting, and all kinds of other goodies. But this reasoning is exactly backwards: the central result in neoclassical economics is actually that competitive private markets are identical to the centrally planned economy. The math says that central planning is not necessary, but says nothing at all about it being worse. Adam Smith's Origin of Wealth was an argument against Merchantilism, not Communism, and argued only that the "invisible hand" acts as if there was an omniscient and benevolent central planner. In fact, Smith argued that there were several market failures that made competitive markets actually worse than a central planner in some ways, and that governments should intervene in these cases.
Of course I will confess that most economists--including myself--do prefer competitive private markets over communism, and "market-based" solutions to market failures over command-and-control approaches. But the neoclassical model actually only tells us that these markets are only "just as good," not better in anyway.
Neoclassical economists have always suspected that central planning actually was inferior, but could not show this in their models. For a long time this was just assumed and not proven. The actual argument for it didn't come until Hayek appeared on the scene. Hayek was one of the foremost figures of the mythical "Austrian School" of economics, whose raison d'etre was to provide an ideological framework against Communism and Marxism, which had risen to prominence in many parts of the world in Hayek's early life. An important thing to note is that while the Austrians called themselves economists and considered themselves the intellectual heirs of Adam Smith, they did not subscribe to the neoclassical economic theory--a mathematical framework which, as I've noted, afforded the Austrians no ammunition in their crusade against communism. Instead, Austrian-school economic tracts read more like something Matt Yglesias might write for Slate--a philosophy essay impregnated with verbal ghosts of neoclassical economics, but none of the math.
Nevertheless, Hayek's argument against central planning is insightful: information is key. A central planner would need to gather literally all information about everything in the economy--an implausibly difficult task that governments--or any other entity simply cannot coordinate. There are two sides to this: one is that because data collection is costly, we waste real resources by attempting to collect the relevant information to supply to our central planner. The cost rises exponentially with the accuracy and detail we seek to obtain. The flip side is that without total accuracy and complete detail, the central planner will make mistakes, wasting resources by allocating them in less than optimal ways.
Information is also key to the efficiency of private markets. But markets have a peculiar way of divying up this information that is not available to the central planner: the price system. In the textbook case of a market with no failures, prices convey to consumers all of the relevant information about the supply of those products, while simultaneously conveying to suppliers all the relevant information about the demand for those products. A single datum--the price--contains all the same amount of information in the private market as the reams and reams of data required by a central planner to make an optimal decision. This means that markets benefit both by exponentially reducing the costs of data collection and by reducing the incidence of mis-allocation of resources. This, and nothing else, is the reason why capitalism is generally better than communism, why market-based policies are preferable to command-and-control approaches.
The lesson of all this is that when designing government policies, information is key. This is exactly the premise with which Mirrleesian analysis begins, so if you are weighing in on public policy and haven't read James Mirrlees or any of the subsequent research, you should stop talking and go read.