And it's mostly limited to fiction, drama, and poetry! It omits almost all math, science (including social science and history), and philosophy that's not of literary significance. Even within those restrictions, it's by no means a comprehensive list of every worthwhile work or author ever (if nothing else, the "Western" qualifier makes that plain).
We're even there for film, and we've only meaningfully had that medium for ~130 years. One may watch thousands of movies without ever leaving the realm of "widely regarded as excellent, meaningful, and/or important". I'd imagine there's far more than enough very, very good recorded music that it's in the same situation. Many lifetimes of top-notch media exist. Reading/hearing/watching anything that's not very good is entirely a choice.