Injustice: As a system state, wickedness is rewarded and kindness is punished.
Abstract: Prudence morality implies justice and justice implies prudence morality.
Justice, especially in the short term, is not a naturally occurring element. It must be consciously produced and maintained. A justice factory consumes resources to ensure the kind are rewarded. This is necessarily a just act, meaning the justice factory too must be rewarded. As a result, a just society is one where justice is prudent.
The justice factory cannot reward itself because it is not a perpetual motion machine. Appealing to a sovereign for justice is thus imprudent, as it is attempting to create perpetual motion. Sovereignty and justice are independent; the sovereign can reward themselves because they are sovereign, not because they are just. Similarly this is the fundamental reason why Mandate of Heaven cannot obtain at the object level; it is a fantasy, hoping that justice and sovereignty are magically linked, instead of having to be linked by intentional and ongoing effort. If you expect God to do all the work, at least have the decency to pray for it.
Instead the 'just society' is the exactly correct wording. The Justice must be voluntarily rewarded by the society which the Justice maintains justice for, because they are just. The hobbits must worship and sacrifice at a worldly temple. (Typo: wordly temple. Get it?)
The Justice does not necessarily have to be rewarded monetarily. (Though this choice restricts Justices to the independently wealthy.) The Justice can also be rewarded socio-morally. Perhaps Justices have the right to lead rebellions. Not the legal right, you understand. Again, the Justice giving themselves legal rights is a perpetual motion machine: it cannot be done. It is the moral right, or the customary right, or the social right. Would personally name it the philosophical right and call it a day.