> The free market is deliberately engineered to push down price to cost of production
The free market is not deliberately engineered for any particular goal, except the free trade between parties. Fundamentally, it's a trading and information system.
Technically speaking, market prices only seek an equilibrium point between supplier and consumers. While, due to human ambitions, there's an empirical pressure for commodities' prices to go down, human labour is different. In case of commodities, you can scale all aspects of productions as long as there are enough. Whereas commodities are constrained by environment, human labour is constrained by the environment and ethics, as you can't just produce people, a hard requirement for human labour. As such, I find that the only cases in which people will be paid subsitance wages are when there's a oversupply of workers and an undersupply of businesses.
> So I am not sure how you imagine free market for labor to help workers unless you assume a market failure of some sort.
Because restricting worker/employer relations only makes it harder for switching firms, which empirically favors the more scarce side, which normally is the employers. Making these firms coops doesn't prevent lack of control, as elaborated bellow.
> The individual share of worker within a coop might be low, but it's still better than 0 under a private (capitalist owned) company.
The thing is, shares on their own are not ownership proper (the same applies to publicly traded companies, BTW) as it's exclusive. A share is percentage of influence over a corporate process that determines the final allocation of the corporately-owned resources. While the share division might be quasi-continuous, the final decisions are discrete and made by the corporation, for the corporation. In the context of a direct democratic governance, everyone will get a vote, but this vote will only translate into control if it falls in the required majority of a decision. In practical terms, having 1% share doesn't mean you have 1% control over the resources of the company: if a worker consistently fall under minority over all elections, they have effectively 0 control. Alternatively, they might find themself having their way in all elections. Despite having the same shares, two worker may have different levels of influence over the corporation. And that's just direct democracy. Indirect democracy, seem in large worker coops, make this distribution of control even messier. Ultimately, this is all to say that worker coops are still private corporations in the sense that they both alienate individual workers. The details of this alienation may be different from traditional individually owned private corps, but this is not the path for worker freedom. For disenfranchised workers, their only option is to find another corporation that better aligns with their values and goals.
Also, value getting redistributed to workers isn't exclusive of worker coops. Stock options, ESOPs, etc. aren't exactly rare in other private corp formats.
> 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
How so? In a free market, the only ones actually dictating the conditions is the supplier (the worker) and the consumer (the employer). The employer is the one providing the job, so they are involved by definition. The market often informs the employer in their decisions, but this influence is always consented, not forced. (Also, one cannot consent to their own death, no need for labor laws to state that.)
Finally, not sure why you just freely mentioned Hayek without elaborating. I also would like a citation, for the only reference I got was:
> There are, undeniably, occasions when the condition of employment creates an opportunity for true coercion. In periods of acute unemployment, the threat of dismissal may be used to enforce actions other than those originally contracted for. And in conditions such as those in a mining town the manager may well exercise an entirely arbitrary and capricious tyranny over a man to whom he has taken a dislike. But such conditions, though not impossible, would, at the worst, be rare exceptions in a prosperous competitive society. (Hayek 2013: 204)
It should be noted that Hayek would consider such dismissal coercive if the action was to result in the unemployed's ruin. As such, wouldn't call this a defense of mining towns.