Yes, this is very enlightening, and we are very fortunate. You won’t see this kind of explanation anywhere else, at least not in English, as far as I can see.
Not too long ago, I heard a very common explanation from a long-time “vipassana meditator” of kāyānupassanā as being mindful of bodily movements, and the formal practice of it is walking meditation:
One walks slowly, is mindful of one foot lifting the ground, moving forward, touching the ground again. The meditator does this over and over, walking up and down a meditation trail.
I suppose this does calm the mind down, and this calmness is often mistaken to be removal of defilements.
Finally, @Jorg, if you haven’t read this old post, you will enjoy it:
Anussati and Anupassanā – Being Mindful and Removing Defilements
Here, Lal delved into the word anupassanā (and also anussati).