Contractor jackers!
Yeah, after this many episodes in, I already see Sougo as... a blank piece of paper. His supposed history is that he is very good at history. But how in the original timeline that born Oma Zi-O that he came upon those powers? I think this is a part of a lesson Sougo needs to be brought in to reflection and he can determine himself what unwanted destruction he caused from a neutral perspective (Tsukuyomi). Geiz is that guy that thinks outright destruction onto destruction is the best negating solution.
Woz... well that is the most (should be) intriguing part of it all. If Sougo is supposedly a good fountain of history learned thus far in his classes, then he would know that the foundations of organization has "those guys". Why did it not stick out for him to show some remark to Woz in some subtle manner other than naivety? That is the biggest problem and that contributes to the reinforcement of the episodic writing that Kamen Rider (not just this series alone) seems to be stuck doing motorcycle wheelie dirt donuts in a field.
I think your inclusion of the Faiz and Kaixa duet is a more fitting summary of what Zi-O is...