Free market, in a typical situation, has the advantage of having more raw computing power, simply because every person uses their own brain to optimize for themselves. And (some people believe that) the benefits of this additional computing power overweight the costs of not having this computing power coordinated, thus wasting a part of it. (It also has the advantage of having local information, having access to this information before it was filtered by political processing, etc.)

But technically, we are speaking about a linear increase in the computing power here. Like, a few million people, instead of a few dozens of government experts. Computational complexity typically does not speak about linear factors. -- Thus you have sinned against the narrow meaning of "computational complexity". I believe the downvotes reflect this.