Consider instead the shift of body weight that started this thread. The body is a column that buckles in the middle. Weight shift is integral to balance -- along the line of the four legged stool with the two legs missing. It is an imperfect image hoever, because the tops and bottoms of legs of the stool are limited universal joints. Statically the whole apparatus should just teeter over to the side.

The thing that keeps us upright is a miniscule gyroscopic sway of the hips in a chaotic figure eight pattern that dampens the toppling sway caused by gravity.

We are always swaying between falling one way or the other. Irimi, done properly is simply arranging the sway to will that fall in the right direction to move laterally. Tenkan is willing the fall with a turn of the hips -- allowing the natural turn of the hips for balance to have its head and reorient in response to applied force.

Kokyu tanden ho allows the manipulation of the rotating/oscillating hip sway and thus affecting the opponent's weight distribution and transfer. In katate-dori I usually sense two forces - 1) an inward push and 2) an upward or downward rotation forming a plane of action. Whether it is upward or downward the plane is the same. My simultaneous response is a 1) lateral shift of the hip and arm, either opening outward or cutting inward, and 2) a torque of the arm and hip in a right or left spiral.

Which one is not really important -- the resulting plane of action is the same. This converts the motion of the forward translation and up/down rotation vertical/forward plane forming the attack -- into a phase-shifted rotation/translation in the lateral/vertical plane. It results in kuzushi because the shift of the attacking rotation into another plane is now out of phase with the balance sway system and thus almost immediately overruns its support into shikaku (one of the two missing legs of the stool).