I used to land at basically this analysis myself, but there are definitely some assumptions that need to be addressed. We can probably agree that to a significant degree “money is power”, or at least, money can elicit power, especially in terms of directing the actions of the desperate. We witness in our society - which is not pure “free market capitalism” - that inequality is rampant. There are theoretical explanations for this blaming both government intervention and just simply the behavior of individuals within the market that centralize wealth. And, conversely, there are theoretical explanations for how government can decentralize wealth, or how market participants can decentralize wealth (including boycotts, unions, etc.). The biggest challenge with this age-old “communism vs. capitalism” debate is that establishing overall tendencies for state vs. private actors requires exhaustive historical analysis, and is not even inherent to the nature of either actor, i.e., someone as a private actor, or state actor, can act in a way that either centralizes or decentralizes wealth. The only overarching principle you can even safely state is that the actions of a state are distinct from those as a private actor because of the “monopoly on violence” factor, i.e., the ability to enforce unfair demands that people can’t escape in practice (a behavior that leftie types usually accuse capitalism of, inversely, by pointing to corporate monopoly power - which of course, depends on the dictates of a state or equivalent body to enforce).

The only way I was able to resolve the problems with this whole analytical framework - communism, capitalism, state, private - was to reject this terminology entirely and perform the analysis in terms of individual behavior, actions, inanimate vs. animate, and the ethical properties deriving from those. A “state” is a useful abstraction at times and a confusing complication at other times. “Capitalism” and “communism” as terms have no universally agreed upon definition, resulting in unproductive, endless, circular debates. What we’re really trying to do is design a social system that maximizes outcomes for every criteria we like - equality, prosperity, individual wellbeing, health, lack of environmental externalities, etc.