Nowadays we see genres of music such as Folk, Pop, Rock and as such that are very different from each other. But when we see music by Beethoven, Mozart, operas, etc. and we categorize those as Classical music. This might give off the impression that music wasn't so diverse back then.
So, I've been thinking about this question a lot lately, and I believe it's more of a music/sociological question than one of history. Furthermore, I think it begs a discussion, not really a definitive answer. 1) there's the directed sociological aspect in dividing up the genres 2) There's the place of genres as a social construct and 3) Differences between and within genres, a underestimation of the diversity found in so called "classical music", and our current relationship with older music.
The range of genres can probably be better attributed to segmentation of the market. If you've heard the word "tween" to describe the age between childhood and teenager, then you'll know that this was a deliberate marketing invention to make a new "genre" of society at whom they can direct products to buy. So perhaps a sales-driven trend to segment musical styles at each and every turn is responsible. As well as the people themselves. Music seems to be tied in with individual identity today more than ever, so making sure the specific style of clothing/subject matter/dancing/instruments used is identified is more important than before. Sort of a, us vs. them thing.
So many genres. Folk, pop, rock. Okay. But did you know apparently there's... Rocksteady? (a less energetic version of Ska), death 'n roll? (a mix between death metal and rock 'n roll), bubblegum pop? (over-produced pop by unknowns for teens and pre-teens). Folk, pop, rock... Very different? Who says? And relative to what? To a non-listener, jazz might sound all the same. Folk and Rock are pretty similar to me - the more you know, the more distinctions you can make. [For me, to use two very well-known examples, the differences between Beethoven's '9th symphony movement 4' ("ode to Joy") and Beethoven's 'Für Elise' are likely far greater than any two rock and folk songs you put before me. I'd be looking at harmony, melodic development, tempi, expressiveness, overall structure etc.; things that would be fairly similar in folk/rock/pop songs.] Having said that, you and me, we'd probably not even accept that there's a difference between J-pop and K-pop. Or that "Viking Metal" even exists. But they do... This is called "social reality". If you deny the existence of the state of Israel, does it still exist? Or that the US dollar is worth what it is worth? This kind of existence depends on whether it is accepted or not. If people say there's an Israel, that the US dollar is worth this much, that Nerdcore isn't G-Funk then... well... I guess it's both true and not true.
So, suppose the difference between a given genre and another genre is that the subject matter is more political, or darker. And the instruments less electrified and distorted. Maybe the singing is less in tune - a bit hoarse. But you can find such differences in classical music easily. Classical music has so much variety, it's incredibly hard to even know where to start. The way the great composers will come up with a melody, cut it to pieces, re-arrange it, put it over different harmonies, on different instruments, at half speed, double speed, change keys, once... twice... move on to COMPLETELY different sections of music and maybe, just maybe at the end, they'll give you a little taste of that familiar melody again just before they finish the piece of music. Ah... (And that's just [a single] melody!) Sadly, this is where the lack of in depth music analysis can lead to assumptions that classical music isn't varied. Furthermore, when we look at classical music, often it is just to study it, so ironically since there's so much diversity, we actually need to SIMPLIFY the groupings. Added to that, the fact that Classical Music can be cut up merely by things like ensemble used (choral, chamber, string quartet), the composer (often, you'll speak only of Beethoven's work, for example, in a way that contemporary singer/songwriters are not regarded, as if he is a genre of his own).
tl;dr? It might be that there's a "trend" to label music styles, but since we look BACK on classical music, the traditions of what the genres of classical music are, are already in place. There's no need to cut it into tiny pieces either for marketing or for self-identification, just because a genre "exists" doesn't make it more or less valid or informative of the style of music, indeed, it might be more of a reflection of the social forces around it and the related dances/clothing etc. AND there seems to be a huge under-estimation of the vitality and diversity of classical music, which is mind-boggling varied and complex - the way one can't even fathom how big the universe is.
This is more of a discussion, so maybe this response belongs elsewhere?