Well because I went through asking folks their headcanons for Ghouls purring, I'll share some of mine. Included half humans, Quinx and artificials for the heck of it
Basically can't because of Trauma or Trouble in development:
Eto Yoshimura(Sen Takatsuki), Tooru Mutsuki, Arima Kishou, Ching Li-Hsiao, Karren Rosewald
Tendency not to even in fitting situations:
Ayato Kirishima, Kurona Yasuhisa, Ken Kaneki, Shirazu Ginishi, Kuki Urie, Jiro, Miza Kusakari
Mixed on purring:
Touka Kirishima, Uruka Minami, Nashiro Yasuhisa, Ken Kaneki Final, Hairu Ihei, Furuta, Touma Higemaru, Shinpaisen Aura, Yomo, Itori, Tatara, Rize Kamishiro
Actually enjoy purring:
Hinami Fueguchi, Roma Hoito, Sasaki Haise, Saiko Yonebayashi, Uta, Kazuichi Banjou, Naki, Nishiki Nishio
For some specific headcanons of what may trigger a likely quick slight sound of something that could resemble purring: Deja vu of safe familiar situations
For the likes of Eto and Tooru whom basically lacked these safe familiar situation, an accidental encounter when they could fit one of those molds of a happy family may trigger it. Like say the absolutely rare occasion of her, Tatara, Naki or Miza being like familiar with her feeling "safe" as the "creepy sister" role, the sudden noise would probably freak any of those three out shattering the kind illusion and in a sense saving her from that involuntary reaction.
Where as Tooru Mutsuki finding some actual safety and friendship as the kind brother inbetween the Quinx and Haise, he may unwittingly too let out a sound that resembles a purr. Unfortunately for him, since noise would likely worry his teammates more whom would try to help him from which further comfort may trigger further noise.
For all the half-humans and artificials it would serve an uncomfortable reminder they're not quite human. Otherwise I'm sure Hairu would love being able to purr.
As for who would do it most as distress, because of of how much struggle and distress she faces and the fact that unlike most I think she'd choose to not regulate the noise. Saiko probably spams angry or frightened purrs.
As for the strange pick that likes it, from his past with his family, sister and eventual attachment to Kimi. I think Nishiki would end up being pretty happy to purr whether in happiness or aggression. Is probably embarassed when a friend like Touka tells him he resembles a cat more than a snake though.
