In regards to socialist/communist confusion, OP primarily refers using the term "socialism", except at the end where they use "socialist communist countries", likely referring to the self-proclaimed socialist countries that strive/strived towards communism. (I'm not sure FEATTATEATTN means here)

> There is, for example, no free market for nuclear bombs or for human children, and for a good reason.

Reasons that don't contradict OP's: "Free markets typically stop being opinionated beyond the concept of enforcing contracts/consent." Nuclear bombs only current purpose is indiscriminate eradication of human life and child trafficking is well... child trafficking. They all break consent. The same can be said about slavery, but not labour.

Which brings to the core of this discussion: the free market of labour. The addition of the free market of labour cannot, on its own, result in loss of self-control by either party. Removing it, however, rewards those who benefit the most from the current arrangement, which is most likely to be the employers.

While commodities, and other conventional properties, indeed do not have a will of their own; once appropriated, they become an extension of the will of their owner. With this in mind, labour, capital and commodities aren't different: neither the human actions applied to make bread, nor the machines needed to make bread nor the bread itself care about their prices or how they are used, but their owners do. In both cases, the same human freedoms are being affected in the same way. Slavery is special because the traded resource in question is another human being, someone capable of self-ownership, and the slaver isn't simply dictating on, for sake of simplicity, non-essential part of their body as with labour and commodities, but the slave's whole body and life, thus violating the consent part.

Which segways to your final paragraph. When I mentioned "worker-ownership", I was specifically alluding to worker coops. They not only do not prove what I said untrue, they, both theoretically and empirically (but mostly theoretically, yet), prove it true. One empirical part is the fact that Mondragon's increasing reliance on contractors, for instance. But, more interestingly, is the fact that, presuming that all ~70,000 Mondragon employees are members (they aren't), each would have around 0,0014% share. Given that Mondragon works under indirect democracy, this share doesn't even translate to direct influence. Is this painting the image of worker emancipation? Notice how the corporate power over the individual is still strong - sure smells like capitalism, as defined as "control by those who own capital", except "those" here is a corporation, which is not that different from today.

Given that you brought the slavery, likely for the analogy with wage-slavery - trying to fix workers by making their employers democratic is like solving slavery by making their slavers republics. The proper solution is to give direct private ownership over the means of production to all, but that's likely economically infeasible (but who knows, society where everyone is a capitalist like this would be neat). However, we can fix the issue with coops previously by keeping them small, but to handle the large contingency of workers and their diversity, a lot more coops would need to exist. Furthermore, these coops would need to be able triage workers that fit into their culture, and worker would need to be able to chose coops that satifify them. That implies a free market of labour. It points to the issue being more located in the concentration of power on people, not individuals, which means socialism can't do anything to fix this, specially if it implies getting rid of the free market of labour. Perhaps pushing for coops can help prevent corporate power concentration, but a healthy free market of labour is critical.

> The addition of the free market of labour cannot, on its own, result in loss of self-control by either party.

I disagree with this, and it's less true in theory than in practice. The free market is deliberately engineered to push down price to cost of production. In terms of labor, it means your remuneration will be reduced to subsistence wage, and not more. An apple doesn't care about its price, but price of your labor determines your living standard and your freedom.

And where this doesn't happen in the real world, it is actually a consequence of labor market failure, for example, labor negotiations through unions.

(There are also other labor market failures that prop the wages upwards, for example for CEOs.)

So I am not sure how you imagine free market for labor to help workers unless you assume a market failure of some sort.

The individual share of worker within a coop might be low, but it's still better than 0 under a private (capitalist owned) company. Moreover, all the value produced gets redistributed to the workers, not just a portion. (And I agree here that outsourcing Mondragon is bad.)

> That implies a free market of labor.

No it doesn't. Free market of labor is more than just a free choice of job, it also means that people who are not involved in the job itself might dictate the conditions of production (for example, it implies no labor laws, so you might die in the summer heat as a consequence). And it is by design.

(I was appalled to find that Hayek defended mining towns. Freedom to change the job my ass!)