As another commenter indicated, this is not necessarily both possible and efficient to do with any known model of a computer. Also, to the extent that market economies provide consumer and elite wants and preferences as inputs, they are morally superior to command economies that provide only the elites' wants and preferences as inputs.
Consider: if no model of a computer can solve price setting, how can the market? Is the market some kind of hyper-computer? (If you think the answer is yes, I encourage you to publish this work, as it'd instantly upend both economics and computer science.)
The market is effectively a distributed computation. It does this by splitting up the intractable problem of solving prices across an entire economy into multiple loosely coupled optimization problems. This allows for a parallel computation to happen. We call these individual computations "firms" and "organizations" and "individuals." There's no technical reason a command economy can't do the same, unless you have a definition of command economy that amounts to "anything that uses a stupid method to calculate prices."
The latter part of what you say is on-the-mark, but it has nothing at all to do with the computability of prices. Simple tip: just because someone points out a basic error in a critique of command economies doesn't mean the person thinks command economies are great.