That doesn't really explain the popularity at times of clicks-and-beeps music and some other modern music.

Sure it does! The listeners of such music have listened to lots of other music, and have developed a mental model of it that is overly predictive (too compressible) to be interesting to the information-seeking machine.

It is also possible that people are listening to the music for reasons other than the music itself (community, feelings of superiority, etc.)

A thing it’s simple patterning. Listen to the same random music on a cd and it becomes a pattern. The more discernible the pattern the more popular the music.

When you say clicks-and-beeps are you talking about music like Skrillex, Alva Noto, Aphex Twin or do you mean something else?

Either way, it sure does explain the popularity. If you consider it as predictability instead of compression, it might make more sense. Listeners have an expectation on what music sounds like and popular music is going to ride that line between the listeners expectations and something more original and stray from those expectations.

I think this could also be why AI music is so bad, because it can hit the listener's expectations, but the ways that it strays from them are seemingly random, which is why a big reason to why it is so uncanny.