"Free market economies"? Like the Gilded Age with child labor, zero pollution regulations, zero drug regulations (Do you know why Coca Cola has its name?), zero laws governing monopolies, military units attacking worker protests and strikes and on and on. Ever hear of the Triangle Shirtwaist fire? I don't think the number of people killed by "free market" economics can ever be determined but I'm sure that it is more than a couple hundred.
The list of victims you listed here probably number in the few thousands. Those figures also exist alongside the pace at which the institutions of free markets, elected governments and the rule of law increasingly pull horribly poor people by the millions out of their conditions. As far as we know, it's the only scheme that has ever worked to do that. On net balance, I'd say the western world has luckily stumbled upon the right way to organize societies. Of course, you may credit some government programs for spreading around the wealth markets allowed to create as a libertarian nirvana is nowhere to be found on Earth. It doesn't mean that all such programs do what they supposed to do, on the other hand, but from a bird's eye view, we seem to be a fairly lucky bunch against the background of human history.
Nevermind that socialism has never really been much more than a label used by authoritarian dictators to cover what their systems actually embody.
I do not understand this obsession with people desiring to appropriate themselves the label of socialism given the horrendous publicity it conveys among historically literate people. However, I don't wish to rebuke your claims on a matter of semantics.
The general problem with what most people call socialism was roughly the same problem with what most people call fascism. In both cases, the intention was to instrumentalize the State at the service of a social vision. People who called themselves socialist believed conflicts within society hinged on the privileges of a bourgeois class and that most of our social ills would die along with the class structure if only the workers would manage production collectively. In practice, this eventually meant that the State would manage the means of production and that all rights of individuals were discarded in the name of the social vision. People who called themselves fascists were not much different given that most of them were actually socialists. The disagreement hinged on the collective appropriation of the means of production: fascists allowed you to keep your business, but you had to use it to serve the State. Save for the racism and antisemitism of Hitler, I am sure many people on the left today would have loved the man. He was all about public housing, public programs, public services, and even environmental protection. He expanded pages upon pages of speech railing against financiers and bankers, saying they were worthless thieves that contribute nothing to society. Mussolini wasn't very different, except he wasn't nearly as racist or antisemite and he wrote extensively in socialist publications.
It is because they did away with the concept of individual rights and liberties that tens of millions of people died. They repeated the mistakes of the French Revolution on a massive scale. The key to making things work is to commit to respecting individual rights and liberties and to place this protection above the power of governments in a way that is irrevocable. If you place government power, or the power of anyone for that matter, above those principles, I guarantee you misery, poverty, sickness, and mass murders will ensue. That's just human history everywhere all the time, save for a handful of countries over a little more than a century. Thanks to limited government and an increasing concern for individual rights, wealth was created and spread further and faster than ever before.