Classical music is much more popular today than in it's 'own time' though it is true that a professional classical pianist is no longer a composer per definition, which one could say was almost true in the past. On the contrary, the two have been totally seperated.
The question is silly, actually. Though it kind of depends on what is meant. Yes, everything that is 'shocking' or 'impressive' has been done. Maybe things that are considered 'innovative' or 'fresh' have also been done. But surely one can write an endless amount of music. The limit will be the number of people in the world.
The problem is that people are not interested. People do not want to hear someone composing a work as great as Beethoven but with a more modern touch. Why listen to a Beethoven-like work that was written by someone obscure instead of by the great Beethoven himself? A work without a history, a legacy, tradition, anekdotes, importance in the evolution of music that we already know, etc.
A short time ago there was a topic asking about what would happen if all the known classical music was somehow gone, deleted from reality. From one point of view that would be great, exciting. People will start writing music again because then there is a need for it.
Mainstream classical music limits itself to 30 composers or so. They rest is largely ignored. People that listen to classical music aren't that interested in the music itself. They want the experience.
Maybe they should ban the public performance of these 30 composers.

I guess this is really the disadvantage of composed music over improvised music.
And since when is Cage's 4'33 about music?