Cultivators at the peak stage of Heavenly Immortal can indeed replace the will of the heavens with their own and execute divine punishment on behalf of the heavens.
However, there is a significant precondition: the compatibility between the Heavenly Immortal and the realm in question.
The size of the realm and the rules it tends toward both impact the process of the Heavenly Immortal's will replacing that of the heavens.
The original Yomotsu Hirasaka, born within Hell's tributary and possessing the Netherworld's authority, with the 10th Hall Yama using it as a conduit to smuggle countless Hell specters, belonged unequivocally to the deep dark Netherworld.
And although Yomotsu Hirasaka exists between reality and illusion, its mass is not enormous—it is, at most, just a Tiny Diverse World.
Such a world almost perfectly fits the Heavenly Immortal Realm's ghost deity who has set foot upon the Netherworld Path.