The state does not exchange labour for labour.
Also, c m c' means dead capital, as in machines. A planned state does not need to use use capital to produce to sell for money with which to buy more capital. It directly commands labour and what is to be produced. It can create capital without needing to make a profit because it can litterally print money to command labour, and any "profits" gained are just destroyed. That's the basis of mmt. It's basically just shit labour vouchers that people can exchange on the black market.
>That is true of every capitalist state that controls the production of fiat currency.
Not a refutation because the whole point is the combination of directly commanding all mop while also being the issuer of currency.
>but it still must provide them with the means of subsistence
Same as above, I don't see how this refutes my argument
>It serves the capitalist in precisely the same way
It does not. Corporations are bound by their limited access to currency to command labour. They have to produce products, sell them, then use the money to hire people again. This is why we have unemployment in crises, because corporations have limited currency, are unable to sell their goods and this unable to hire workers to keep production going. That is also why it is the government that then steps in as the issuer of the currency that then uses its money printing ability to hire all idle labour, thus unjamming the machine of capitalism. There is a clear difference in the role of a currency for a private corporation and the role of a currency for a government. A government is not bound by a profit cycle. If it miscalculated and uses half of all labour to create useless junk, it will have no long lasting impact as all labour can be instantly shifted, while in a capitalist economy the loss of sales would mean half of all employers are unable to hire workers.