I presented the tri-tether above, mentioning Assessment of an Alternative Concept for a High- Altitude Wind-Power Generator publication, and some information and also some expected advantages.
Now I will try to explore what can be the disadvantages. I made an analysis on What is possible with Payne's patent US3987987 figure 5? and on some previous posts. Said analysis also stands for the tri-tether configuration. As shown on figure 1 from the publication, the tether network is fully connected. The kite force (decomposed into a force in tethers by kite pull and a force by crosswind kite motion) acts simultaneously on the three anchored tethers composing the tether network. As a result a significant part of the force is not used to rotate the generator, and the tether network acts as a yoke preventing the kite from taking full speed.
A mean to overcome this issue would be conceiving a rig inspired by OrthoKiteBunch where only one tether is transferring the kite force in the same time. Winches and their active control would be required. Here is a sketch below: