Think of it this way: if you're going to be using computational arguments against central planning ("there is no way to do the planning in a straight mathematical form"), you've got to remember that you're really just talking about an algorithm that computes a set of prices. Markets implement such an algorithm by breaking down a economy into parts that are only weakly coupled, and solving the pricing problem within that particular market. There's no technical reason that a central planner can't do the same. The central planner faces the same issues with nonconvexities as the market does, but you can at least match the same set of prices.