This might seem like nitpicking, but it is hardly the case that music is only performed by the ones who write it. A few examples:

• You're probably thinking of old classical dudes like Mozart whose works have been played ever since he first penned them. These classical composers still exist. Modern composers for orchestra like Michael Daugherty have their pieces played across the country. Composers for choir and wind ensemble like Eric Whitacre or Frank Ticheli are practically superstars in their respective circles. While this music might not define our era, it's far from gone.

• Much of the music "from back then" that comes to our mind first was written for ballets or operas. This musical tradition is still quite active, and rather familiar to most people. We all know John Williams' Star Wars themes or his alternating half-step Jaws motif. Composer Andrew Lloyd Weber and lyricist Tim Rice have become wildly successful with Phantom of the Opera; you might not know composer Claude-Michel Schönberg, but many people will instantly recognize his songs from Les Miserables.

• While many artists and bands do write their own material, a large number do not. Folks like Max Martin are professional songwriters that you'll never see on an album cover, but are just as influential on the pop scene as the artists themselves: just take a look at all the number one singles Martin has written or co-written. The music industry is heavily dependent on folks like him. And of course we can't forget cover songs. Any successful modern recording artists can expect to see others playing their songs; just think how many Beatles covers are out there, let alone how many Beatles cover bands there are.

On the other side of things, there are folks like Chopin or Paganini, who we often think of as composers for piano and violin, but were in fact rather popular performers and virtuosos on their respective instruments. Thus, I'll argue that your question is based on a false assumption. Especially with music, we like to periodize history to the point that an era's defining genre becomes its only genre. Modern American pop music simply cannot trace its roots to the symphony hall; while Beethoven was busy conducting his Romantic masterpieces, everyday folks were singing ballads and drinking songs and working songs in the fields and by the hearth. Likewise, while Taylor Swift shakes it off on the arena stage, John Adams is busy writing minimalist orchestral tributes to those lost in modern tragedies.