As others have indicated, kokyu dosa is treated as an exercise in our dojo.
It's a case study. It allows us to focus on subtle body mechanics w/o confusing footwork, hand exchanges, etc.
Before we "get it" it's dang near impossible to move a resistive uke. Once we do "get it", it's so easy that the danger is in getting lazy.
Our way of finishing kokyu dosa bridges uke's near-side elbow over our near-side thigh.
Since I, personally, enjoy exploring the interaction between judo and aikido, I will sometimes transition from our finishing position to ude gatame.