In "Everybody's Business" by Abba Lerner, the market-socialist economist, he makes the case that markets are efficient for distribution and allocation of resources. The example he uses is the anarchist/socialist reforms in Catalonia during the Spanish Civil War. They tried to peg the price to the cost of production and ban speculation. It turns out that relative scarcity driving up price and speculation helped ensure that food stores lasted throughout the whole year. Speculators would buy some up and set it aside to sell in the winter. Without the price mechanisms and speculation, the food stores were exhausted during the spring and summer and the people were left without enough resources to make it through the winter. Lerner also alludes to "the democracy of the market" but holds that such democracy only works if wealth is relatively evenly distributed. The market is not democratic if one person has a lot more money (a lot more votes) than another person. Markets cause inequality to rise if left to themselves. This is why you need rules for wealth redistribution in order to correct the failure of markets to be democratic.
Also, generally speaking, insurance is always a market failure, as is healthcare provision. Which is why we need single-payer healthcare and the nationalization of homeowner's and car insurance.
Btw, I checked out your page. I really liked your take on immigration. Following now.
It is mathematically proven that pure chance leads to "the rich getting richer and the poor getting poorer" (ever fewer getting ever more, ever more getting ever fewer).
If you want to prevent this, you have to do something.
Immigration: Just ask how many genereations you have to go back to no longer be an immigrant, because we all are somewhen in time.
Yes, that's why redistribution is necessary for markets to work well for everyone.