Why indeed? We don't pay for food each time we reap the benefits of the nutrition it provided down the line. Weightlifters don't pay royalties to protein powder companies. It could be argued that artists could also be expected to not be paid beyond the initial creation of a work. It would be a very different world to be sure, but it's not a given that it would be a worse world.
"I can't think of any good reason why music should even be copyrightable."
This particular argument is about whether music should be copyrightable.
We often don't know which songs are worth millions and which are worth tens until years later.
If we believe that people who write songs should be compensated roughly proportionally to how valuable their songs are, it is hard to think of a way to actually do that which does not involve compensation long after the song is written.
Especially in light of the fact that copyright is not fulfilling it's intended promise. Specifically that the government protects the work for a time, and in return the work goes into the public domain after a reasonable amount of time in order to enrich society as a whole.