I believe Kako's backstory is either not completed or a twisted version of the truth and should not be taken at face value.
Aidairo loves to make a mystery tell us "their story" the second Nene get familiar with their boundary:
And later reveal that either the story was a lie that's is convinient for the mystery to achieve their goals:
Or a lie that haunt them to their core, until it twist the meaning of their existence:
Considering how Kako's whole story is basically a "don't mess with time. It will ruin you. Human weren't built for it, only I can't handle it." leaving a lot of things vague or quick to be dismissed. I think that while he is revealing many true things about his existence, he is still hiding the full story or twisting the details so that it makes his message to nene "give up, only the guardians should control time," more clear and heavy for her.
I would genuinely be surprised if aidairo doesn't re tell this story later under a new lense, because it feels imcomplete.
We don't actually know what this special thing is after all:
The story want us to believe this special thing is either Mirai, or the hourglass, but I don't quite buy it...
A yorishiro is always central to a mystery story (Tsuchi with the moon rock. Yako with Misaki's scissors. Mei with the sketchbook she was drawn on... so on) and Kako never once mentioned this key or the clock that the key unlock.
EDIT: We also don't know how Kako built Mirai/whose soul she has, since the niece no longer exists. Or why he choose a human as a keeper of the present.
For as solid as Kako's story is, something about it feels very odd.
