I understand this question is very specific, but it's confusing me. The standard layout for US-engineered coups is, resources are nationalized, the US and domestic corporations engineer a coup, and resources are re-privatized. Except in Chile, that re-privatization never occurred. So how did Pinochet come to be seen as a bastion of hope for capitalists, if copper remains nationalized to this day in Chile? Is copper a unique case?
Was the Chilean coup less about nationalization and more about containing the Soviet sphere of influence?
You're factually wrong in your question. The fact is that the market became wildly liberalised under Pinochet. What was a part of the public sphere or the commons was ruthlessly sold out to private interests. As soon as Pinochet came to power the US sent a squadron of economists, all of them from the Chicago school of economics, famous for being a major school in the development of neoliberal economics. It has been said by plenty of economists and historians that Chile (and in some ways Indonesia) was a neo-liberal experiment.
Source: Harvey, David. A brief history of Neoliberalism.