It was this "Why didnt the US try to emulate the British Empire?"
Well they did, but they came really late to the game.
In principle the major obstacle to US expansion was that they were hemmed in by European powers in the north and an independent Mexico as a rival to the south and on the Pacific coast. Then the Royal Navy controlled the Atlantic and Caribbean (which was a double edged sword since they both helped the US not deal with European powers, but prevented any conquests of their own) and their own attempts at carving out spheres of influence in the Pacific were interrupted early on by the Civil War, and then the expansion of the European powers in Asia, which meant the US had to opt for economic concessions rather than territorial concessions instead when aiming to get in on the China game.
The one big overseas imperialist war was a walkover, but internal politics (and the cost of subjugating/administering the Philippines) soured many Americans as well. So instead American Empire became slightly less overt. They mostly scooped up little atolls and islands, with the one big imperial prize in the Pacific being Hawaii. Through the WWI period they began treating much of the Caribbean and Latin America as protectorates, and occupied and overthrew governments as it suited American interests, the Banana Wars were just imperialism lite.
The United States didn't establish an enormous overseas empire for a lack of particular will, but rather they failed to because they could not challenge the existing empires and were late to the game itself.