Board Thread:Theories and Speculation/@comment-28518855-20170711204016/@comment-5085906-20170711220711

My theory is that this particular dojutsu only awakens on individuals who rely heavily on it. We had two ancient Otsutsuki characters who possessed the Byakugan but didn't awaken a Tenseigan; Kaguya and Momoshiki. However, both of them also possessed an extra dojutsu (RinneSharingan in Kaguya's case and Rinnegan in Momoshiki's case). That could be the reason why they didn't awaken it like Hamura did.

Kinshiki probably didn't awaken it because his bloodline is distant from Hamura's bloodline, which would come to create the Hyuga clan (and apparently awakening the Tenseigan in modern times requires a Otsutsuki+Hyuga mix). Though, and I know this may veer a little bit off topic, there are a lot of feats displayed by Kinshiki that would only make sense if he had the Tenseigan or at least a different, more subverted form of it. He can create weapons, similar to how Toneri could create a cage to keep Hinata out of Naruto's reach and in the manga, Sasuke assumed his strength was being increased by some kind of jutsu.

But anyway, yeah - that's just pure speculation.