We commonly accept that the kingdom of heaven is organized along familial hierarchies. In some sense, God is legitimately our God because he is our Heavenly Father. The priesthood authority is often passed from father to son.
Likewise on earth, we have a tendency to organize ourselves into tribes which are often defined by descendancy from a patriarchal figure. The nation of Israel is all the descendants of Jacob/Israel. The tribe of Judah is all the descendants of Judah. The Edomites are all the descendants of Esau/Edom. The Nephites are all the descendants of Nephi. etc. But this tribal association is solely an earthly phenomenon, because the patriarch dies. In heaven, the patriarch is alive and can rule his tribe, but on earth he dies, and someone else needs to take the seat of authority, at least if we are not to devolve into very small familial units whenever a grandfather dies.
There is a heavenly order when the patriarch rules over his direct descendants, but what legitimacy is there for an uncle to rule over his brother's descendants, or for one who is distantly (if at all) related to the members of a tribe to rule, and moreover, to pass the authority to rule over those he is not related to down to his sons and heirs? We see many instances of the ruler taking on the name of the patriarch, in order to put on the air of the heavenly order or things, as when the kings of the Nephites are all called Nephi (Jacob 1:11), the rulers of Egypt are all called Pharaoh after the father of that nation (Abr 1:25-26), and even in Rome all the emperors were called Caesar after the founder of the empire. In the middle ages hereditary succession and primogeniture were called the divine right of kings.
But all this putting on airs of the heavenly order is merely a counterfeit of the heavenly order, and because it is a counterfeit, it is easily perverted into an evil practice. These issues are carefully considered in Mosiah chapter 29, and he concludes, "because all men are not just it is not expedient that ye should have a king or kings to rule over you." (Mosiah 29:16) A famous historical example of the failure of hereditary rule is the five good emperors of Rome, when Rome had five good emperors in a row, which is so difficult to accomplish because hereditary succession tends to hand authority from one who has worked hard to earn it down to one who has been raised in privilege and who often abuses his unearned authority. The first four of the five good emperors (Neva, Trajan, Hadrian, and Antoninus Pius), kept the form of hereditary succession while actually placing a good and worthy successor on the throne, by formally adopting the chosen successor, so that he could be the son legally even if he was not truly a hereditary son. When the fifth and most famous emperor, Marcus Aurelius, broke with this legalistic fiction of hereditary succession, and let his real son, Commodus, take the throne, the result was unspeakably bad.
If we consider that hereditary succession might not be a legitimate ordering of earthly authority, can we find any scriptural support for doubting it? Certainly for the most common form of hereditary succession, primogeniture or passing authority to the firstborn son, there are many counter-examples in the scriptures, such as Jacob, Joseph, Nephi, Saul, David, Solomon, etc. So even if primogeniture is a pattern in heaven, since Jesus Christ is the firstborn of the Father, it is not therefore to be blindly copied in earthly succession.
What about hereditary succession in general? Is it just for only one descendant of the patriarch to have rule over the entire tribe after the patriarch's death? To answer this question, I will go to the most fundamental doctrine of Christ and Christianity, and observe the pattern we find there. In John 3, Christ himself teaches, "Marvel not that I said unto thee, Ye must be born again." "Except a man be born again, he cannot see the kingdom of God." "Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God." As we said at the beginning, God rules us because he is our Father. What happens when we are born again? We become the children of Christ.
"And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters." (Mosiah 5:7)
Christ is King of kings, and Lord of Lords, but kings exert their authority through power, violence, and force, usually over their enemies. In like manner Christ will need to exert authority over those who decide to be his enemies. "For he must reign, till he hath put all enemies under his feet. The last enemy that shall be destroyed is death." (1 Cor 15:25-26) Christ will subdue all things, but we seek not to be his enemy, nor even his servant, but to be born again as his sons and daughters. And when he has subdued all things, then he can cease to reign, because the heavenly order is restored. "And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that God may be all in all." But then Christ is both the father and the son (Mosiah 15:2-4), being the son of heavenly father, and also the spiritual father of all those in the kingdom of heaven.
"Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power." (1 Cor 15:24)
The whole purpose of Christ being king is for him to put down all earthly authority. In this respect no earthly system can be considered to have the mandate of heaven. God may choose kings such as Cyrus or David to bring about his will on earth, but he is clear that we should have no king other than him. Moses and Mosiah instituted a minimalist government, with no executive, traditional laws which required no legislature, and only judges to resolve disputes. When the Israelites wanted a king instead of judges for their government, this is what God said about it. "And the Lord said unto Samuel, Hearken unto the voice of the people in all that they say unto thee: for they have not rejected thee, but they have rejected me, that I should not reign over them." (1 Sam 8:7)
When the need for all rule and authority and power is over, what remains? The only ruling power left is the love and respect between parent and child. And when Christ no longer needs to reign as king, what does he do? That is, a kings reigns, but what verb do we use to describe what fathers do? We do not choose our parents or our children on earth, so your father is your father simply because he is your father. Perhaps this is why the Father states, "I am" (your father).