There will always be someone who owns something. A system will simply not work without an administrator. There is nothing in communism that prevents it from working, except there is however humans and their nature. and since power corrupts, pure communism will likely never work. There's an expectation that everyone will play nice and not take things for themselves, when if that is not the case the system crumbles. If everyone owns everything then someone will step in and take it from everyone else, especially when the boundaries are so poorly defined. It's in the nature of predation. Capitalism acknowledges the natural tendency for greed and predation, embracing it and regulating it.

So in my opinion we should have an outlet for competetive and predatory behaviour in our society, working with it and not against it as it is rooted in our nature.

With high taxes the state funnels a lot of money from the private companies. Money that goes back to the worker or is in the workers benefit. Instead of money staying stagnant within companies. Which is what seems to be the biggest issue with pure capitalism, hoarding and stagnation. With democracy and no lobbying these companies also don't have a whole lot of power over the state.

You are also right, denmark is not communist in a traditional sense or perfect for that matter. But it is communist in the sense that value is delegated to the laborer if they should fall on hard times or if they should become injured. There are also powerful unions with knowledge of the industry, which workers pay to protect them from their employers. There is always a net to catch you, no man is left behind and everyone deserves to live. I think that is somewhat communal. Even if everyone is not equal.