Most of the "great" symphonies stem from the 18th and 19th centuries. Shostakovich was the last great symphonic composer and he died in 1975. I'm not aware of anyone writing great symphonies since him. Doesn't anyone try? If Haydn could churn out over 100 symphonies why can't modern composers even manage one or two?
Symphonies were historically commissioned pieces of work. The commission was to pay for the writing and then the performing. Commissioning for symphonies has mostly disappeared so orchestras are not likely to take on new symphonies in their repertoire. Shostakovich composed under the commission of the Soviet State and they requested symphonies to be written.
So why won't orchestras take them on, typically? Because now orchestras realise that they have to sell seats. Old symphonies are familiar so an audience will be looking forward to it. New symphonies are unfamiliar and. . . they don't sell as much. Orchestras are having to adapt and in recent years they have been having a little resurgence of success by shaking up their repertoire. Less symphonies and more soundtracks from movies and videogames.
So with that, no new symphonies are being made. There isn't much demand for them.
That is not to say that symphonies are still being written and being performed. It's just that money isn't being diverted to these endeavours as they used to be.
All musical forms, from Gregorian chant to hip hop, are most closely associated with a particular time and place, they go in and out of popularity. Older forms become a niche product, created and appreciated by a select few, not the masses.
The problem with symphonies is that they require a full orchestra, and thus are one of the most expensive musical forms possible. So they cannot survive as a niche production. I'm sure people still write them, but it isn't financially worth it to produce them if only a few people show up to see them. Paul McCartney wrote a symphony recently --he's wealthy enough to self-finance an orchestra, and famous enough to fill seats --but it wasn't considered "great." (You can hear it here if you are interested.)
However, as Phillip suggested, new symphonic-scale work is still being commissioned, created and enjoyed --on the soundtracks of big-budget movies and video games. If you're serious about your orchestral work being actually produced, and you aren't McCartney, these days you are probably marketing yourself as a soundtrack composer.
There are still symphonic compositions being made but most are created as scores for movies. John Williams is one of the most prolific soundtrack composers, writing scores for Star Wars, Indiana Jones, Superman, and a great number of pieces that are embedded in the modern culture. I had the fortune of attending Star Wars in Concert and the experience was as grand and dramatic as any traditional Orchestral performance I've attended.
Hans Zimmer is another great composer for modern orchestral pieces. Download the Dark Knight Soundtrack and prepare to be blown away as you realize just how significant a role the music plays in the overall experience of the movie itself.
There is a lot of symmetry between today's orchestral compositions being made for movies and the Operas of the past.
I think you have to distinguish between different aspects of a symphony when addressing the "demise" of the symphony in contemporary music. A symphony is among other things:
- a large-scale work (usually 30 ~ 60 minutes)
- a large-scale work (requiring 50 ~ 75 musicians)
- written for a more-or-less standard selection of instruments
- made up of 3 or 4 parts with different tempos and moods
From my personal experience of composers that I like and concerts that I go to, I would say that contemporary composers still write works with some of these features, but rarely all four at once.
There is no shortage of large-scale (long) works. As an example, Tristan Murail's "Les Sept Paroles" from 2010 is around 52 minutes, and many of his more recent compositions, like "Légendes urbaines" (2006) and "Le Désenchantement du monde" (2012) are around the 30 minute mark, as are e.g. Unsuk Chin's Violin Concerto (2001), Cello Concerto (2008) and "Mannequin" (2015).
There is also no shortage of works written for large orchestra; most of the examples above are for large orchestra, and "Les Sept Paroles" is for large orchestra, choir and electronics.
The standard selection of instruments is where contemporary composers start to deviate from the traditional symphony form. As modern music moved away from the 19th-century traditions and started experimenting with novel sound colours and electronics, composers started to choose instruments that fit the ideas of the composition, rather than writing compositions for a specific ensemble, like a string quartet or a symphony orchestra. A modern composition may be played by 50 or more musicians, even with tradional instruments, but sound nothing like a 19th-century symphony. Even relatively traditional composers like Messiaen would write large-scale works for a non-standard selection of instruments, like "Et Exspecto Resurrectionem Mortuorum" (1964) for an orchestra of woodwind, brass and percussion, but without strings.
The traditional symphony form, with its three or four movements with different tempos and moods, is probably the aspect that you are least likely to see in modern compositions for orchestra. As new ideas about musical structures emerged, like the interest in "process" in Murail's early work, where a musical idea would be introduced and then transformed in an organic rather than in a theme-and-variation kind of way, the structure of compositions started to be seen as a result of the musical material and its development, rather than as a pre-defined form that composers forced their material into. If traditional forms are still used, it's usually those forms that were not very strict anyway, like the concerto; you'll find many contemporary works described as "violin concerto" or "cello concerto", simply because any sort of composition with a solo instrument and an accompanying orchestra can be seen as a "concerto", however modern or unusual its structure.
To directly answer your question, I don't think there's a lack of people who are able to write a decent symphony these days, it's just that composers' (and to a lesser extent musicians' and audiences') interests have shifted away from the traditional 19th-century symphony.
Musicians make music with the technology available.
Do you think if Beethoven were alive today that he would scoff at the intricate variations in sound possible with modern equipment, and stick with piano music only? I don't think so. The same applies to the symphony composers you mention.
Imagine creating beautiful music in a stream of pure ideal creation. Now imagine having nothing available to make physical sounds with except for different sizes and shapes of sticks. Could you still make beautiful music? Of course you could. It would just all be made with sticks.
If you were then given a variety of instruments to choose from, would you still use only sticks to make music? Maybe, but I doubt it.
Of course some people would continue to make music only with sticks, but note that they would be choosing to use sticks, rather than using sticks because they have nothing else.
Several hundred years ago, there was a far more limited range of sounds available from the musical instruments of the time. Music written for orchestras had the great advantage (over any single instrument) of making it possible to combine such a range of sounds in a single aesthetic piece of art. In other words, if you wanted a wide range of sounds in your music, you couldn't write for a single instrument.
Today, people still do write symphonies for traditional orchestras, but there is a wider range of choice. To simply create music with a wide range of sounds, it is not necessary to involve an actual orchestra. So people choose other things.
You're not looking at any strange disability in modern composers; as others have pointed out there are composers writing symphonies today. What you're looking at is an increase in the number of choices available to musicians.
I am puzzled by the basic assertion that there are no great symphonies from the twentieth century. This page, https://en.wikipedia.org/wiki/Category:20th-century_symphonies, lists several hundred symphonies written in the twentieth century. Of course, one can argue whether they are "great" or not but I would consider any of the symphonies written by Bernstein, Elgar, Furtwangler, Shumann, Khachaturian, and Stravinsky to be 'great'. Perhaps the question should be why you don't consider them "great"!
Not every work we think of as "great" today started out that way. Greatness moves with fashion. If you closely listen to Beethoven's Ninth and compare it to what was being written at the time, it was light years away (I won't use relative, judgmental terms like "ahead") from any of its contemporaries. Initial reaction was mixed, with many of the lesser composers of the day (I'm looking at you, Hector Berlioz) severely trashing it. Conversely, much of the popular symphonies of the day, (again, you, Hector) have never regained their initial popularity.
As well, much of what we consider "greatness"can also be laid to our familiarity with the structural forms, such as sonata form, which repeats, changes, then reaffirms the original melodies. Mahler started taking this apart in the 1900s: serious composers swooned, but the public was a lot less thrilled (se above comment about popularity). His symphonies were largely unplayed until the 80s, and are now very often played - it's possible that movie music has flexed our aural narratives (the stories, images, and feelings our minds create when hearing music) to the point where Mahler is now coherent - we can hear the story inside what we used to consider noise. Since the teens, composers have been rewriting the forms of symphonies - I don't have a good handle on how to characterize it, but it seems (imho) to be a loose collection of microburst themes and feelings (except for P. Glass). I have a poor musical memory, so I can't recall contemporary music themes in the same way I can the older classical forms. So much of contemporary music doesn't appeal because our aural narrative just don't speak the language, even though we get the feeling.
A lot of my thinking in this post was sparked by "All the Rest is Noise," by Alex Ross. It's the biography of early to mid 20th century music.
Because commercialization has degraded and cheapened the art of composing music for orchestra. Second, technology and software enables music composition, playback, and editing without necessarily having to have a virtuoso orchestral level of playing skill with an instrument.
With my Roland synthesizer I can compose and mimic the sound of an entire orchestra playing and you wouldn't know the difference. Why invest the time, effort, expense, and logistics of getting all the players of an orchestra together, to meet to play in a concert hall, manage the booking of the concert, sell tickets, scheduling, parking, recording, copyright, etc., when all this can be done at home with a powerful PC, a synthesizer, and high fidelity recording equipment.
I can choose the genre, and I can network real-time with other players across the Internet for over the Internet live performance and rehearsals.
Times have changed, no sense in living in the past.
Like all other genres of music and forms of art, classical composition goes through trends. In my opinion, we're actually in the direction of more "accessible" classical music, as listeners - common folk and scholars alike - grow tired of over-complicated, academic, "intellectual" composition.
You'll find that composers still do frequently write traditional forms - symphonies (of which Arvo Part has 4, Philip Glass has 10, John Corigliano has 3, to name a few more prominent examples), string quartets (Ligeti wrote two, Carter wrote 3 very important ones, just about every composer has, on some level, worked with the medium). In academic circles, there will always be a demand for sonatas and concerti.
There are two major reasons why this perceived shift has happened - one is a certain freedom from form that dates back as far as the romantic era, with composers like Liszt popularizing tone poems and other free forms, Berlioz pushing the boundaries of established forms and realizing some very thorough programmatic music, so on and so forth. Sometimes, the musical idea that a composer needs to/wants to express simply doesn't work in a traditional four-movement form. The other major reason is that classical composers rarely write in the tonal idiom of pre-Romantic music either. Tonality has grown, it has evolved, it has even been dissolved (atonal and 12-tone music), there is no reason for a modern composer to limit themselves to boundaries that are 200 years out of date.