The arguments mentioned here go something as follows. "Businesses (in the free market) centralize resource control, therefore centralized control of resources works".

I hope you realise that using the fact that a business survives in the free market by using strategy A as an argument to prove that strategy A works implicitly supports the free market as a tool for selecting efficient strategies.

Moreover, libertarian free marketeers readily admit that on a small scale centralized resource allocation cannot be avoided and is likely very efficient. For example in the family unit no one would dream of applying free market principles to a great extent.

I have also read your own article trying to disprove the economic calculation problem. You seem like an intelligent person, which is why i was sad to see that you misrepresent the problem and accordingly disprove a misrepresented statement of the problem. The problem is not that a unit for calculation cannot exist. The problem is that a value can not be attributed in any useful way to such a unit. This is a very different problem.

Then you use the labor theory of value to try and disprove this statement, which does not work as the labor theory of value is easily disproven by an example. The labor theory of value roughly asserts that :

"The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it."

If this were to hold you would have no objection to me grinding planks into dust as opposed to turning them into chairs as long as it too the same amount of effort. Clearly nonsensical. Less simply put, the labour theory of value asserts that we will always have constant returns to scale, which is clearly not true. If I flood the market with chairs the value of the chair decreases, but it still takes the same effort to produce.

The remark that labour is a determinant of price is definitely correct. To conclude that it is the only determinant is observably false. The easiest way to deal with this is to abandon the labour theory of value and accept that the equation that determines value is multivariate and labour is just one of the variables.

In conclusion you misrepresent the problem then use faulty theory to disprove it.