Denmark is much more decentralized. The same sort of policies adopted in Denmark would work less well in the US, because we are much more centralized, and hence far less democratic (if you define democracy properly, where people can affect their government.) Denmark has nothing like the LA school system or the McAllen, Texas, Medicare system.
I think that from a libertarian point of view, the number one structural problem in America is scale. Spending per government entity is the product of spending per constituent times constituents per entity. If we had higher spending per constituent but many fewer constituents per entity, we would have a healthier diffusion of government power.
How could the U.S. operate like Denmark or Switzerland? Imagine the U.S. carved into 30 sub-nations of 10 million people each. At the national level, we would definitely have a common defense and foreign policy, plus a supreme court. Otherwise, see how much we could devolve to a sub-national level: health care policy, public pension policy, education policy, environmental policy, trade policy, monetary policy, financial regulation...if you say that's impossible, look at Denmark.
Each of the sub-nations would have state governments, just as the Swiss have cantons. Each state government might have 400,000 constituents. A lot of government responsibility would be devolved to these state governments. Each of the state governments would have local governments--again, that is what the Swiss have.
I am not saying that we should jump to this structure. However, we should be able to imagine it. I think that devolving power from Washington down to 30 sub-nations would give us 30 times the number of experimental models for issues like health care and education. That would make it more likely that we would find the most successful models.