That magical Nordic system is called "social democracy", it's of course rooted in socialism, and it's so old that one of the first dark memes amongst left-wing groups ("You killed Rose Luxemburg!) is about them.
It's strange how those who say the Nordics aren't really socialist will be the first to dismiss their policies as socialist when they're suggested for the US.
They have free markets and businesses, doesn't sound like a socialist system to me.
You're thinking of Communism. Socialism doesn't imply government ownership and control of the economy.
Neither does communism. Communism implies ownership and control of the economy by the people at large, but the presence of a state is, supposedly, a transitional phase.