Let me do some research into Danish policy before you get carried away with how free of a market they have. For instance, it is true that Denmark allowed the privatisation of primary education, but only 13 per cent of the primary education students receive education in the private sector. The thing you should realise is that modern socialists do not view the free-market as a malady.
For instance, in the UK, the Labour Party (Democratic Socialists) ensure that every citizen has access to health care through the National Health Service, but you are allowed to purchase health care privately if you so desire; and in fact, many people do purchase private health insurance plans. Modern Socialism is all about filling in the gaps the market system causes.