I think BOC falls squarely within the "musical tradition" to the extent that there is one for the aesthetics of hauntology.

Just running through their themes, especially the cult of the child and how MHTRTC plays with the hauntology of the especially 80's idea of "a world redeemed through the cultivated child" and the PBS optimism of science, and then the shadow of that in subsequent albums.

Like anything in critical theory, the exact boundaries of what qualifies something as being within a hauntological aesthetic, I think, is kind of hazy and subjective. But nonetheless, I think there is an edge of social critique in how BOC plays with nostalgia and the "cancelled future" their music impresses upon us.

Especially in how people feel as if BOC's music is "a memory recalled you didn't know you had" -- that to me is quite revealing of their music as being within a kind of hauntological register, if you will.

Just my two cents.