For what it's worth, I just read an English translation of that story, and the cats could be metaphors for students' various approaches to, or reflections of students' respective levels of ability within the IP/IS training models, as well as within internal arts.
Conscious thought is depicted in the story as a detriment to attaining supreme skill. Yet, when students are learning IP/IS, the mind is so poor at "internally" motivating the body that, ironically, the body, e.g. the hands, is externally used as a crutch to help lead the mind (such as in forms, and to assist with opening the body in standing exercises). The ultimate goal isn't to be "centered on technique" (the black cat), "fac[ing] down opponents with overwhelming ki" (the striped cat [who states that his techniques are unconscious, but then is admonished by the Old Cat that his techniques are conscious]), or "harmonizing with everything" (the other old cat). So, the paradox is that there is much conscious training involved to reach a point that the body is sufficiently transformed for the cat/student to negate an attack or thwart a defense upon contact, while having the luxury of mushin as a de facto state.
As for the cat that sleeps all day: perhaps the cat keeps a .45 hidden under his bedding, and the local rats are smart enough to steer a wide berth.
Right, there is much conscious training involved to reach the level of the striped cat. This conscious effort is, not really a detriment, but a cul de sac on the road of attaining supreme skill.
The notions of negating an attack or thwarting a defense are representative of striped cat thinking! If that's how you view the world then everything is about attacks and defenses. Swordsmen of the early 1700's were apparently wary of thinking this was true skill.