I keep reading articles and seeing documentaries that use expressions like "Rome was much more diverse than we thought". I've seen the same applied to Athens and London. Now, I know I am not a degreed historian, but I kind of find those statements to be a bit strange, and in many ways a little disingenuous considering the international reach those cities enjoyed. Rome made a habit of incorporating the culture of conquered foes into their own. London was a port city with international trade.
Does the idea of diversity really surprise people so much, or is the emphasis on these things reflect our current political landscape more than the reality of times?
I'm not sure that you are on track that "historians are surprised" by this, but rather that there are many things in popular media that are written about ancient diversity that take a surprised tone, because often people imagine ancient societies to be fairly monolithic. You can see that sort of thing happen here, when for example a movie or a TV show depicts people of color, folks come here to ask questions about it:
https://www.reddit.com/r/AskHistorians/comments/enfo2s/in_the_movie_1917_the_2nd_battalion_of_the/
or, in animated films:
or even in commercials:
https://www.reddit.com/r/AskHistorians/comments/f38n8j/is_black_vikings_a_thing/fhhnez1/
or video games:
I suspect you are correct that much of this is driven by our current political moment, with conversations over f.ex immigration policy that are way out of scope here, but I think it also goes further than that. Consider for example services such as 23 and Me, which purports to tell you your ancestry based on your DNA, which it compares to people living in places with current political boundaries that do not map neatly onto what we know about migration, population flows, etc.