It was a fixation of literature, history, and political science, for… oh, centuries. Not unjustifiably, either. Any entity that becomes that immensely powerful and influential is gonna tend to cast a long shadow. It’s hard to take even a shallow look at a solid millennium of European history
after the fall of the Western Empire without running into at least allusions to Rome all over the place. Longer than that, probably. Like you poke at 20th century European history a little (“why was Alsace-Lorraine a point of contention for Germany and France?”) and before you know long you’re talking about Rome.
“But why Rome, of all ancient empires? Why so Eurocentric?”
Well, the short answer is the Industrial Revolution started in Great Britain.
If you mean why right-leaning groups are interested in it: I’d guess it’s the narrative of barbarians threatening from beyond the borders, the cautionary tale of how that and internal corruption brought them down (“well that’s a bit reductive…”—look, I know that), the honor-culture stuff (real or imagined), et c. The more intellectual side of the right in the US (though I think they’ve been rather left behind at this point) may be interested because of connections to the founders, like Washington’s Cincinnatus-like rejection of power after two presidential terms (we named a fairly major city after the dude, even)