Every single day, the problems in America show us why nation-states function better.
America is a nation-state though?
A nation state is a state intended to serve as the homeland of a particular ethnic group or collection of ethnic groups.
Germans, Italians, Swedes, etc. are ethnic groups. ''Americans'' are not. That's the fundamental difference between America and the countries of Europe.
America is absolutely a nation; it has a nationaly mythology, symbolism, an idea of what it is to be American and of what criteria must be fulfilled in order to be American, a collective national identity that states that the Americans are a people with the right to national self determination.
Just because the American national identiy is more recent, does not mean the USA is not a nation state.
Likewise, ethnicities are not mutually exclusive; and just because the USA as a nation is made up of multiple ehtnicities does not mean that there is no American nation. Similary, just because the definition of what it is to be American is less exclusive that other nations, it doesn't mean that there aren't certain criteria that exist.
The USA isn't even particularly unique in this regard, as
most ethnic groups are composites of different ethnic backgrounds, just often in the more distant past.