Well said: “Mussolini’s Fascism was a form of Socialism despite the fact the State merely controlled the means of production and did not own them. This false distinction is usually made in arguments that Fascism is a right-wing system, when in fact it is a form of left-wing Socialism.”
Hitler’s Germany did not seek to own the means of production, only to direct the owners to follow the dictates of the Party. The key element of a Socialist System is the Centrally Planned, State controlled economy.
Since no amount of Bureaucrats can send orders throughout the economy in anything like as efficient a manner as the laws of Supply and Demand send price signals through a Free market, these centrally planned economies always fail, regardless of the political rhetoric used by the Party leader to secure control.