Markets allocate resources efficiently. In the long term, in large enough scale, on the average, and with a high probability. But the scale is often not that large. In many fields, a small number of companies dominate the market, making it susceptible to groupthink. When business leaders are biased in the same way, the market is also biased. Once in a while, we get a bubble that way.

Because value is ultimately subjective, the efficiency of the market depends on how you weigh individual value judgments. If each dollar gets one vote, efficient resource allocation looks different than when each person gets one vote. Markets tend to favor the former. Regulators like to think that they moving the needle towards the latter. Sometimes they manage to do that, and sometimes they move it in a completely different direction.

Assuming that you're right in thinking that in the free market—presumably to the exclusion of other way to organize economy—prices function as signals that steer (or influence, or regulate if you will) activities of the active forces in that market: where do you get the reassurance that any and all signals for demand are consistent in their relation between desirability and profitability?

I think the USA are a good model for how you do not want the raw unbridled power of money regulate everything. At this point the USA are politically a failed state, and if the present regime goes on for much longer, the welfare of the people will suffer even more.

The US has the most expensive health care system in the world, yet everyone except the top few percent is constantly risking bankruptcy from illness, and despite the staggering amounts that people have to pay for their private ensurers (that are not meaningfully kept in check by laws and do not experience competition from public insurance options), figures like infant mortality and life expectancy do not look rosy. Because the US has a freer market than most other countries, higher education has been made ever more expensive, to the point it has become virtually unobtainable for many.

As for "the gray, soulless stagnation that defines every controlled economy", I want to hang that on my wall next to a picture of a Detroit suburb.

Those were the loud voices advocating for free markets everywhere.

Unregulated free markets don't necessarily produce great outcomes for society. E.g. suppose free markets in certain sectors naturally result in one company becoming an entrenched monopoly. As a monopoly it can stifle competition, and limit innovation (why waste money on RnD if it's not necessary to stay ahead of competition?) while extracting monopoly profits, to the detriment of consumers and society at large.

Another example is the general trade off between efficiency and robustness (including national security concerns). With a free market, individual firms in your economy make cost optimising decisions to switch to use cheap imports, but you might end up depending upon cheap gas imports from Russia or cheap manufactured goods from China. If those dependencies end up very hard to change (e.g. if domestic suppliers go out of business as they are not cost competitive), you end up with your whole country's economy in a poor bargaining position.

Unregulated free markets also don't make decisions that are optimal for society in terms of how they account for externalities. What is optimal from the perspective of a profit maximising company owner or shareholder can be suboptimal for society as a whole. "Privatise the profits, socialise the losses". The whole global warming thing is an example of this -- cumulative CO_2 pollution emitted from economic activity hurts everyone in the world, both people alive now and future generations, but in the absence of enforced regulation, people (both producers and consumers, everyone involved in the value chain from mining coal to us folks consuming electricity to fuel our ranting on the internet) can participate in economic activity that causes CO_2 pollution and gain a piece of the upside but shove the diffuse downsides onto everyone else who aren't involved in the transaction. Having something like a globally enforced carbon tax that got priced into short term profit optimising decisions made by market participants could give better results for society - the problem is how do you get there from here.

Another point to consider is that supposing a particular free market is more efficient or more beneficial "on average", there are always specific groups who are going to be winners and losers. Different groups benefit or suffer in different ways. E.g. free trade, free movement of capital without free movement of labour and low cost transportation costs allowed higher cost domestic manufacturing to be replaced with imports from another country with lower wages. In a change like this, some groups benefit and some groups lose, like domestic manufacturing workers who no longer have anywhere to work. If the groups that lose out have political power they may push back to reverse this trend.

I'm not trying to argue that centrally planned economies are great (there are some historic examples of gigantic calamities caused by this, famines in the USSR etc), but the "free market" if left unregulated also produces a bunch of failure modes that are suboptimal.

That's an idealized assumption. Real world economics is full of deceptive signalling and false information.

I'm not sure binary free markets or not is the right framing anyway. Competition is, but sometimes competition means intervention.

Also who's to say what a market is? Isn't a regulation part of a market, but where you include votes as a form of currency?