that seems a bit naive. you can think of it like that, but then you'll find actual practicing capitalists (not capitalism, the generalized concept) will always cozy up to centers of coercive power, until they're the ones weilding those coercive powers. you've basically reinvented the medieval distinction between the church and the secular authority. the church would never burn people alive, they just determine if a person is spreading heresy and the secular authority will do what it will.

in reality it's all one system and it exists in reality. the system that exists in theory is just a model to carry around in your head.