Lassiez-faire works just fine in reality. For price-fixing, behold the example of the Prisoner's Dilemma.
The rundown is that the two are taken to different rooms so they can't communicate.
One can betray the other, and the other is ruined, but they get off scot-free. They can betray each other, and get a moderate sentence. Or they can stay silent and get a light sentence.
Most often, betrayal nets the most, so that's what people will angle towards. Betrayal in this case meaning a price drop.
The laissez faire style of economics is not realistic. It assumes that people and businesses will cooperate with eachother with no problems. The kryptonite of Capitalism is monopolization within industry. If there isn't enough competition, the system fails. The lassez faire philosophy, has no protection against this. And you might here the Communists and others argue that without regulation, who will prevent businesses from discriminating and making dangerous products. Who will prevent businesses from doing unethical things?
Many free-market supporters think that the market will just correct itself. Many think that crooked businesses and people will not be able to survive in a free market. But this was contradicted in 2008. The market didn't correct itself until it was too late and the cause of the crash was crooked business. Specifically in the financial sector of the economy, with its heavy leveraging in subprime mortgages and selling them as low risk when they weren't.
You can argue crony capitalism to explain some failures, which would have some truth to it, but you cannot argue that the cause of the crash in 2008 was government cronyism. And it was the same story in 1929. America moved toward socialism after that. This laissez faire mentality is why we have social security and welfare today.
And I think we all understand why communism doesn't work. Well, at least the soviet style of communism. You cannot centralize everything and expect things to work efficiently. You cannot give the state supreme power over all production and expect no corruption within the government and secret agendas.