If you watch some Japanese videos on pouring sencha (or less noticably in intructions for brewing and pouring) as I am sure you already have, you will see rocking motion already (I did not watch this video however ... yet). The gentle rocking mimics the pouring into several cups. So the rocking is no different than if you were pouring for several people into individual cups, right?
It serves a few possible purposes, one being it can help draw tea leaves away from the screen ... it can also help in releasing flavor.
Also, I agree, the pouring technique(s) can open up the use of almost any good screen for sencha brewing within reason. For asa and fuka I may use an asa sasame, a ball screen, and the wall screen ... oh and of course the stainless steel screens). Yesterday and today I used wall screens (a hagi and a soma) for very fine leaf fuka. And while yes, this releases more leaf into the cup, as long as you do not just let the tea sit but focus on the task at hand ... it is not a problem.
What is the problem with this kyusu? [EDIT: I had the wrong photo/kyusu originally]
To me it appears
that the screen holes may be blocked where it adheres to the pot, a major fatal flaw as the pot can never drain fully. It is best to see open holes right up against the pot! This may be an illusion with this pot, but this is definitely something to look for and an advantage to wall screens.
Shape of the pot can be more of an issue for fuka (as well as less skilled pouring). A very flat kyusu is going to be problematic for fuka because the leaves do not have any wall below the screen in which to adhere to, instead they clog up the screen.
Regarding leaves clinging to the side. I never leave any leaves stranded above water for subsequent brews.
I will give a gentle swirl, or if need be hold my finger over the spout and gently rock to dislodge (I would not do this for a gathering, but for me and the Mrs., why not?)
Regarding fill. I often fill 2/3-3/4 full ... sometimes less and do not have a problem doing this with a kyusu for Japanese greens. I rarely fill a kyusu ... except last steep which I reserve for SLT at night.