Maybe it seems super obvious that 'Murica would be a motif in a speech by an 'Murican president. It's not just that Monroe talks about the United States, though. America is an entity and an idea that represents the opposing force to the powers of Europe. America is both the United States and the new Latin American republics to the south, together against the old colonial monarchies.

Dang. That's enough to bring a red-white-and-blue tear to our eye.

America isn't just a landmass in Monroe's speech; it upholds a certain ideology. For example, when he first makes a stand against further European colonization, he refers to, "the American continents, by the free and independent condition which they have assumed and maintain," (4) shall not be made into colonies again. Well, that's because "The political system of the allied powers is essentially different in this respect from that of America" (12). The republican system that's spreading from the U.S. southward is included when Monroe talks about America.

Monroe also talks more specifically about the United States, of course, as the thing that will be very upset if Europe gets imperialistic: "we could not view any interposition for the purpose of oppressing them […] by any European power in any other light than as the manifestation of an unfriendly disposition toward the United States" (16). America is present even in the final lines:

It is still the true policy of the United States to leave the parties to themselves, in hope that other powers will pursue the same course […]. (26)

Monroe not only mentions America repeatedly, but talks about its relationship to Europe too. His most potent description comes when he explains the differences in government:

[…] to the defense of our own, which has been achieved by the loss of so much blood and treasure, and matured by the wisdom of their most enlightened citizens, and under which we have enjoyed unexampled felicity, this whole nation is devoted. (13)

America's revolutionary history makes it the nation it is today (and by today, we mean 1823), and is the reason it has to stand against imperialism.

The references to the United States (rather than just the American continents) are necessary to accomplish Monroe's goal. The primary objective really is for the United States to take a stand on its own behalf and protect republican systems in its neighborhood. To do that, at least in a speech, the nation and the region have to be invoked repeatedly, not just as territories but as ideas.

Do you suddenly feel the urgent need to listen to "America the Beautiful"? That's what we (and Monroe) were going for.