Denmark's defense budget is really small 3.2 % of government spending vs 18.2% for the United States. Therefore, Denmark has much more cash to spend and is a richer nation relying on US for defense.
The US gets considerable economic and political advantages from that defence outlay. It's quite normal to park a fleet outside someone's capital (in international waters) as a show of political force. It's still a ridiculously high percentage, but the concept of the World Cop needs to be put to rest. It's more like World Vigilante Strongman.