Hi there, as a big big big fan of Shoui x Asari, let me answer your question ^.^
1. Kami can die from overuse. Asari has served since Rikiichi time and Shoui used lots of kotodama as the Head of the family is more than other members (and Asari served Shoui continuously and heavily in 7 years) so the burden is much for his body even ưith maintainance. That's why he đie.
2. Shoui is officially the Head of the family as stated in the Konoe x Kotoha arc and stated again the Shoui x Adari arc, but he chose to reduce and maybe stop using kotodama (at least in the S x A arc), using "Wish of the family Head) as an order 'cause the wish's Head is absolute. Aside from using kotodama, the Head's job includes assigning work for other kotodamashi, negotiations and other paper work. Well from his portrayal he's kinda like the President of a company now so he has lots to deal with even without working as a kotodamashi.
Hope this helps ╰(*´︶`*)╯♡
This manga has hurt me so many times!! All of the characters have broken my heart from their tragic backstories! I love that the story has made me confused so many times by jumping from one timeline to another. I still have questions though, specially with Shoui and Asari's story.
For Kami's to die: 1) their core must be broken 2) be terminated since they serve no master -- otherwise they may live very long and may be passed down from one master to another.
SO why did Shirahase and Asari die? Is it from wear and tear that their lifespan also decreased? Yet, Asari has regular maintenance but still died.
ALSO, I'm quite confused with Shoui. Did he stopped using Kotodama? Asari refused to go with him because he thought he was useless since Shoui doesn't practice anymore. What does Shoui do now? Who's the current head of the Mitou family?
Sorry too many questions. I hope someone answers them. :)