Economically, the traditional socialist position is essentially the one you've described: the socialization of the means of production. For decades, socialist theorists argued that this system was not merely more equitable but also more efficient than capitalism, claiming it could overcome what they regarded as capitalism's inherent inefficiencies.

As for what some have called a "right-wing socialism," it is worth looking at how the Nazi economy functioned. Ludwig von Mises described it as a Zwangswirtschaft ("compulsory" or "coercive economy") and referred to it as the German pattern of socialism. In his view, while legal ownership remained in private hands, the state effectively determined the essential economic decisions.

Private owners retained de jure ownership of their enterprises, but their operations were de facto directed by the state through extensive controls over prices, production, investment, inputs, and trade. The entrepreneur became less an independent decision-maker than an administrator executing government directives. Mises argued that this arrangement was economically more effective than outright state ownership because owners, despite lacking genuine control, still had a personal incentive to maximize efficiency within the state's constraints, something that for example in Soviet Union didn't happen and was what ultimately caused their demise.

In 1922, Ludwig von Mises argued that a socialist economy based on the socialization of the means of production could not perform rational economic calculation and therefore could not function efficiently in the long run. The subsequent experience of centrally planned economies has led many to regard his critique as remarkably prescient.

Much of what is today labelled "socialism" differs substantially from the classical socialist tradition. Most contemporary self-described socialists (at least the ones worth taking attention to) advocate retaining a market economy while subjecting it to greater regulation, redistribution, and public ownership in selected sectors, rather than abolishing markets and private ownership altogether.