Folks in Copenhagen don't care about everyone's quality of life, they seem to care about the quality of life for their fellow citizens. I don't see the Danish tripping over themselves to help the less fortunate outside of Denmark, but many Americans help out illegals who invade America.
I think America could do this but it would require doing something about illegals and like Denmark, getting rid of birthright citizenship and moving towards ethnic homogeneity.
America is too diverse for people to really care about everyone else.