Spoiler... So there is something I wonder...
Is anyone else curious about the Twins from 400 years ago...?
For what we seen in the manga the previous Twin set:
Both Yataro and Asahi were killed by Shimei Higashimura before the battle of Sekigahara.
Yataro died, and did not revive. Asahi died, obtained Kai, and revived but was later killed by an arrow.
From Asa's explanation about obtaining Kai, the Tsugai offered her two options: Accept Kai or stay dead. The Tsugai also mentions upon death Yuru would appear in the equivalent place for Fuu.
Arakawa sensei made a rule clear; Tsugai come in pairs, yet it SEEMS Kai and Fuu are an exception for this... but are they?
Back to the previous Twin set, what if the reason why Yataro, did not revive was due to Fuu offering him a different set of choices? Perhaps something that might impact the Kai twin?
Killing the other twin to obtain Kai and have both sounds... counterproductive to the narrative... of course would complete the Tsugai set but then why would Right and Left exist "separately". I also don't think one Twin is meant to have Kai and Left and the other Fuu and Right (and in this way each Twin counters the other to a lockdown).
Another scenario is that Tsugai are meant to fuse into a stronger one, with Kai and Fuu as the combination of two different sets. This would explain why each pair has a "theme".
I don't think I will keep speculating due to the lack of info but didn't see this discussion in other posts so well there it is... not sure if there is other clue that I missed... I'm loving this manga so much...