The big problem with all these comparisons of countries is that you compare a 320 million people country (USA) with a less than 6 million people country (Denmark). It simply does not make sense, we should compare the USA with the complete EU.
A strong counter-argument would be economy of scale (in education, healthcare, defense...) for example.
It's unlikely that as a country grows, the optimal class size increases or that a doctor is somehow able to treat a patient nx times faster than in a smaller country. Doesn't make sense on the most basic level.
Defense does...sort of, but the US DoD is such a unique and unprecedented beast in human history that it's hard to make hard conclusions about it with n=1.
a caveat to healthcare is that medical R&D probably does have economies of scale, but not routine treatments and healthcare.