There are living composers. I won't give an example because it's just my taste in music. Also, I am not a classical music expert. I listen to all types of music. I am not an authority for any genre.And there are who knows how many great recordings of Beethoven's 5th, many of them with more or less equal merit for potential inclusion. There's only one Abbey Road. There's only one Thriller. Your complaint about not including any classical music is akin to complaining that Breaking Bad wasn't included in a list of greatest movies of all time. Yes, Breaking Bad is a truly great piece of visual art, but it's a TV show, not a movie. Give an example, what is one 'classical album' that you think has the most merit for inclusion?
Beatles, Michael Jackson,...the main instruments here are vocals. Some artists sing what others write.
If your list was 100 greatest works of entertainment you could put movies and TV shows on the same list.