No, capitalism is about capital owners having control about what is produced and how it is produced, and we have exactly that, especially since Friedman "shareholder primacy" theory, which, at least to me, looks like the ultimate form of capitalism (capitalism != liberalism, which is about markets and exchange, not about production methods).
Communist countries however are never about communal ownership of production method. I think there is reasons for that: communism is not only about production methods, but also about the "march of progress" and other philosophical theories that are more or less dumb (some are very effective analysis tools, some are very less so), and communist leaders pick and choose what they want from it.
Why is capital owners controlling production desirable?
It's not. But that the system we're currently under. In a better world, you'd have employees, local government, consumers as well as obligation owners on the companies boards.
Because they created the production; it they couldn't control it then they'd have no incentive to create it and there'd be no non-state-owned businesses, exactly as happened when China was fully communist and still happens in North Korea today. Capital doesn't grow out of thin air just from "working"; the only people who think it does are those who've never tried to build a successful business.
Because of incentive alignment. They are the only ones incentivized not to do something stupid with their own resources.
of course people are also resources in this framework, and "something stupid" could be providing insurance/healthcare/pension etc - unless a tyrannical (/s) government forces them to do otherwise
How does Elon Musk fit into your framework?