I think capitalism can be understood as a living entity, a being composed of billions of smaller beings (people), essentially cells. It evolves (legally and through market innovations), has an immune response (police), and grows and reproduces itself (imperialism). The cells are independent life in their own right, but they exist almost wholely within the body of capitalism and the structure of their existence reinforces their participation in the greater whole of capitalism. All complex organisms are composites of smaller organisms and I think it makes sense to reason about capitalism and how to go about changing it or destroying it from this lens.
I think most people would agree with you but would call it “the economy” since they can’t imagine a non-capitalist economy.
I’m not particularly opposed to calling it the economy, but since I’m starting from the view it should be changed into something else Capitalism fit