Note that large corporations in capitalist economies (and to a lesser extent extremely wealthy individuals) face exactly the same problems with central planning

Note that large corporations in capitalist economies (and to a lesser extent extremely wealthy individuals) face exactly the same problems with central planning as socialist economies do. It's slightly different: on the one hand power is less concentrated (but still highly concentrated), but on the other hand private actors have less incentive to act in the public interest. If we wish to reap the "wisdom of the crowd" benefits of "free market" ideals then we need to make sure that wealth remains relatively well distributed.