Where It All Goes Down
Sure, we're technically in America in "Shine, Perishing Republic," but the problems we see happening there are also the same problems we'd see anywhere else that an empire exists. Whether we're in America or on the opposite side of the globe, there are bound to be mountains and meteors (a.k.a. the stuff that can build up an empire and the stuff that can bring it down). In other words, the speaker is being both specific and universal all at the same time. It's a bit like when a scientist runs a neat experiment in a Petri dish and then explains how the same thing happens out in nature.
Since the speaker uses the word "man" and "mankind" a lot, we also get that he's applying the cultural patterns we see in America to the rest of the world (otherwise he would have said "Americans," or "Yankees," or… maybe "Floridians"). No one's immune to man's pesky habits of wanting power and using corrupt ways in which to get it. And eventually, it all ends up back in Mother Earth anyway, so no country, empire, or ideology is ever so special as to avoid decay and change. We might laugh a bit at the irony of how man goes out of his way to be super-powerful and invincible, only to be reminded that he and his plans are no different from nature's fruit. But alas, the speaker makes it clear that this is the ugly habitual truth folks try so hard to forget (excluding our smart Shmoopers who, of course, saw that one coming).