Classical composition moved in a kind of academic, atonal direction in the 20th century which was completely inaccessible to most of the public, and essentially died, in terms of a popular artistic movement. After Stravinsky, there just wasn't really much left to do. (Composers still write movie scores, but these basically just rehash what was already done in the late 19th and early 20th centuries.)
Instead, the world moved towards rock, pop, hip-hop... and there's a lot of exciting stuff there. Unfortunately, it's mostly based around 5-min songs, which limits its complexity. No matter how genius something like Brian Burton's "The Gray Album" might be, or certain Led Zeppelin songs, the format doesn't allow for even 5% of the kind of complexity that a symphony can embody.
So the Bach's, Mozart's and Beethoven's are surely out there -- but they're not doing the same kind of music, and they're harder to recognize as equivalents because we've abandoned musical structural complexity for sonic complexity instead (it's more about the sound or flavor or texture of a track, its hooks, and so on).
It's not a popular music story at all - pop/folk music has always been doing it's own thing.
It's certainly niche, and painfully so. I think there is some potential for growth, given the absurdity of my aging friends forcing themselves to continue to engage with music written predominantly for teenagers and college students.
But that's a terrible, awful reason to not write music in that old style! If Mozart were alive today, wouldn't he still be writing music in his style? So what's wrong with somebody else writing it for him, now that he's dead. Maybe it's difficult to sell, but still.
Part of why the Classical composers loom so large in our minds is that they were the only "genre" of music available (by the rich modern standards of the term "genre"). We look backwards, and they are all there is to see. Now there's a bajillion genres, and many of them are full of very smart, experienced people plugging away.
I do not mourn this turn of events. I celebrate it.
(And yes, I am well aware that "Western" music is not the only kind and there's rich traditions of music in all ethnicities, etc etc. Still, Western music of the Classical era was something special and I don't think it's amiss to observe that. In the end, what they created was for all humanity, as evidenced by how quickly it has spread to all, and it is not surprising that when we look back, what we see is Bach and his progeny, which includes Beethoven.)
See Gyorgy Ligeti, Arvo Part, John Adams, George Crumb. Phillip Glass, and Nico Muhly. Everyone except Ligeti (RIP homie) is still living last time I checked.
The reason his output is so huge is of course because he for several periods was employed as a composer and had to churn out large number of compositions.
That's not to say that there's not lots of good material there, but it's not like his entire output is of sufficient quality to keep most people interested.
Secondly, I suspect that the situation whereby musicians these days aren't expected to pen a large quantity of compositions is one of the prime reasons for the mysterious shortage of Mozartesque prodigies.