Rather than markets contra communism, I think we should think of it as property rights contra state ownership (of everything). It is because people are allowed

Rather than markets contra communism, I think we should think of it as property rights contra state ownership (of everything). It is because people are allowed to own things that they can trade. In this system there's plurality whereas in a system where all is owned by the state, there's a monoculture. This is why property rights are important to many things including intellectual freedom. However, the "market" can also create monoculture if one player gets too big.