The question is not “how do we draw the line between classical music and non-classical music”, but how do we fix the problem of sorting / organizing music that has a known composer and multiple recordings by different musicians / orchestras.
Even though people play covers in popular music styles, people rarely care about organizing the music that way. I don’t think, “I want to hear Yesterday” and then look up a list of covers. But I do think, “I want to listen to Rite of Spring” and then look up a list of recordings.
Even though composers are a big deal in Jazz, I still usually care more about the performer. Most of the time, I’m not going to ask the computer for a list of Autumn Leaves recordings.