The word you are looking for to define the United States' role is "Hegemony," although some international Relation theorists would argue that the United States is a "Pole" in a Unipolar (previously Bipolar) world system. Perceptions of the role and overall power in International Relations and applicable or inapplicable historic precedents are a long and ongoing debate in International Relations which are difficult to summarize in a Reddit post, and indeed can take up anything between a college course to a dissertation all the way to an entire academic career. If you would like an introduction to IR theory insomuch as it pertains to interpretations of american hegemony, I would suggest a few books rather than going into too many details (although I'm more than happy to answer follow-up questions) I'd also like to keep it short because this isn't, strictly speaking, a history question: historians, in a general sense, prefer to deal with details. International Relations theorists like to make as large generalizations as possible.

A popular view is that the United States had the potential to be the world's military leader immediately after the First World War, but internal pressures favoring isolationism impeded this, and instead the United States only embraced its leadership role in the West after the Second World War. George Modelski in particular, in his "Long Cycle Theory" explained in his 1987 book Long Cycles in World Politics argues that true hegemony is only within the purview of naval powers, who necessarily enter in conflict with weaker land-based challengers: and since the Second World War, that hegemonic naval power has been the United States. Of course, Modelski's theory is problematic; International Relations theorists like to deal with absolutes, which historians are especially good at poking holes in. Modelski's arguments on the long cycles in modern world history: the Mediterranean proto-hegemony of the Republic of Venice, Portugal, the Netherlands, the United Kingdom, and the United States, only really works if you subscribe to his very specific trade-oriented interpretation of what constitutes hegemony, and are willing to overlook his broad historic hand-waving which might not even get past the mod team here on r/AskHistorians. However, it's fair to say that modern academics generally accept that the United States emerged as the leading power of the west after WWII, and after the collapse of the Soviet Union is the single world unipole. But some academics refute the idea of hegemony altogether: Charles Doran, in his 1991 Systems in Crisis, looks at world powers' rise and decline in capability relative to each other over a lengthy historic time series dating back to the early modern era. By doing away with absolutes and dealing only with relative power, the natural consequence is that in Doran's interpretation hegemony cannot exist. States definable as great powers only gain or lose strength relative to each other, and Doran's definition of power (a complex algorithm agglomerating economic and military indicators) does not easily allow for one power to accumulate enough relative strength to go unchallenged as you would expect a hegemon to.

A less theory-based book with more narrative that might interest you is John L. Harper's American Visions of Europe (1994) and The Cold War (2011) which examine the United States' role in the bipolar world, that is to say a world with two great powers: The United States and the Soviet Union.

There's also an interesting feature of post-WWII international politics whereby there are long-standing alliances which, rather than counter a specific aggressor as they did in the past, have proven very long-lived. No one's quite sure why that is, or why the United States' alliances in particular are so longevous, but there are a number of books and papers expressing ideas (which I think are also online). In a collection of essays edited by Doran titled Power Cycle Theory and Global Politics, (2003) there's Chiu, “International Alliances in the Power Cycle Theory of State Behavior,” as well as Walt's book The Origins of Alliances (1987).

A number of articles on the future of unipolarity now that the Soviet Union has collapsed might also interest you. I would suggest the following, which I think are recoverable online in PDF:

B. Posen, "From Unipolarity to Multipolarity: Transition in Sight?," in G.J. Ikenberry, M. Mastanduno and W. Wohlforth (eds.), International Relations Theory and the Consequences of Unipolarity, Cambridge University Press, 2011

and

W. Wohlforth, "The Stability of a Unipolar World," in International Security, XXIV, 1, 1999