- Do you agree that from experience and observation, we can tell that certain genres or fields appear to become completed?
- Does this concept or another concept best explain what is happening?
First of all, Beethoven's "Für Elise" isn't a song, it's a bagatelle; let's get the genre right. (The previous sentence also demonstrates the proper use of the word "genre", by the way.)
The rest of your comment is just a reaffirmation of your confusion of mass culture and culture tout court. I (might) agree that mass-culture's greatness-producing capacities have plateaued, but I don't look to mass culture as a source of artistic greatness, so I don't really care.
If you studied music in sufficient depth, you'd see the possibilities for yourself, and your intuition would switch from "music is almost exhausted" to "mass culture is really poor at generating musical value".
You're failing to engage the question of the nature of songs and music as a metaphysical level. I agree that mass culture and dissemination of works is part of the discussion, but it doesn't seem like you're trying to engage with that nature of "what is a song?". (See a number of the longer comment chains by other posters who provided thoughts on this topic if you're not sure what is under examination besides mass culture and dissemination.)