Non market mechanisms dominate the world, and they aren't just government regulation.
People go into teaching and nursing out of altruism, not because it pays well. People preserve historic collections because they love them.
Nepotism is rife in many organisations, connections and 'who you know' is hugely important, half of Russia's GDP is in corruption, and so are most countries in the world.
In most markets consumers don't actually understand the product they are buying, whether that's technology or consultancy, and cannot competently compare two products and tell which one is better.
Efficient market is a dream, and you should not be dogmatic about it.
I heard many claims of that, but haven't seen any evidence. I've often heard people say they teach/nurse in order to pay the bills.
> People preserve historic collections because they love them.
True, but such collections are not remotely dominant in an economy. Often they exist only because the government pays for them, which is not free market.
> Nepotism is rife in many organisations
If that means an incompetent is running the show, that fits under "poorly run businesses" I mentioned.
> half of Russia's GDP is in corruption, and so are most countries in the world
Corruption is not free market.
> In most markets consumers don't actually understand the product they are buying, whether that's technology or consultancy, and cannot competently compare two products and tell which one is better.
They don't have to. They use advisers who do, there's a thriving industry of people doing reviews, and lastly imperfect information is called "risk" and is priced in to most everything. For example, a used car bought from a dealer will fetch a higher price than one bought through Craigslist, because the latter is riskier. There's nothing not-free-market about risk pricing.
What makes you believe that? That seems like a very strong, very broad claim to me. Almost too broad to even conceivably be true.
Poorly run businesses is why there is always opportunity for someone else to do better, and why there is a constant turnover of businesses.
> There's no real money to be made in breaking the racket, because by breaking it you'd just be paying more for the same thing your competitors are paying less for.
Your scenario means that hiring nurses is a high margin business. High margin means businessmen will be attracted to get into those businesses. (After all, businessmen are in it to make money, not pursue a social agenda.) Lots of businessmen moving in will inevitably erode away those high margins.
This is what always happens in a free market. Greed trumps racism, sexism, etc., every time. If it isn't happening, look for a legal/regulatory framework that prevents it. For example, the original impetus for medical doctor licensing was to drive black and jewish doctors out of business, because the free market had failed to do so.
See "Competition and Monopoly in Health Care" by Frech.