Why do socialist systems have mixed economies?

Socialism is not considered a mixed economy.

Socialism is defined as a system based on public ownership of the means of production, self-management in enterprises, and production for use instead of production for private profit. There are two types of socialism: planned economies and market socialism.

A mixed economy usually refers to a type of capitalism where the government intervenes in markets to affect economic outcomes, or engages in some minor indirect economic planning. Mixed economies are heavily capitalist: profit-driven enterprise is the dominant form of organization, most firms are privately-owned, and markets are still the primary way of coordinating the economy.