I don't think free markets are the ultimate solution. For example, the Irish Potato Famine was made worse by absentee landlords selling potatoes as a cash export crop, contributing to the single-crop dependence and the overall famine.

Similar dynamics occur in bananna republics, the congo, etc... Free markets are great for wealthy countries with lots of functioning social and political institutions.

Free markets have been great at lifting many, many people out of poverty. However, unrestricted free markets can have horrible consequences. Just google for a few examples. Free markets work with functioning legal and social systems. I don't think it's fair to characterize the elimination of poverty as solely due to free markets.