Divine Right of Kings: Why?

European monarchs had to justify their reign. Religion plaid a major role in that context throughout the history of mankind: Having divine approval a monarch had the right to reign, to suppress, to order, to take and to give. Seeking the connection to god(s) political leaders tried to be seen as something divine: People don't question the power of god(s), don't question their decisions (the installation of monarchs and their actions) and don't question their existence. State and religion used to have a intense mutual relationship until the age of enlightenment. Monarchs made use of their power and of violence to maintain their reign, but they also had to made use of divine justification. A good example for that is the genealogy of ancient rulers who tried to create a lineage from the mythical heroes and gods up to their very own family.

So I'm wondering: did people perhaps believe in the divine right of kings partly because anyone who wasn't particularly adept at managing the different wants and desires of his subjects tended to get killed a lot. So the lineage of kings that survived would likely have something in the genes and/or upbringing allowing them to continue on and procreate before someone knifed them in the back.

You're mixing up two ideas there: the divine right of kings, which says that a particular leader is "subject to no earthly authority, deriving the right to rule directly from the will of God", and order of succession, which has to do with who becomes the leader after the previous leader dies.

The divine right of kings is just the idea that as God played an active part in human affairs, any leader must have been implicitly accepted by God, and could at any point be rejected by God (e.g. Saul in the Bible). Thus, if you are attempting to usurp the leadership, you are either conspiring against God (if you fail) or doing God's work by selecting a new leader (if you succeed). At the end of the day, however, the leaders' position was protected by physical force.

Order of succession have gone through lots of different schemes, from primogeniture (firstborn legitimate) to agnatic seniority (next younger sibling) to salic patrimony (divided between relatives). I think your question is more to do with why more societies didn't end up with an order of succession that depended on a new leader being picked by a group of individuals (like Roman consuls) rather than being passed on through hereditary.

The idea of natural selection (1857) and genes (1857 at the earliest) are very modern ideas, so I very much doubt that anybody would have thought about kings having successful lineages as biologists might today. There are also lots of different factors are going to come into play as well: a leader would have the opportunity to maneuver their chosen heir into a position of power, ensuring that they were the most experienced to take over when they died; or a leaders' family might be popular with the people being lead, who might turn to them when looking for a new reason.

An interesting example of effectively-but-not-officially-hereditary succession is Augustus' settlement of 23BC, which granted Augustus a bunch of legal powers and titles which were previously held by several different people: when Tiberius succeeded him in 14AD, Augustus had already granted him the powers he would need to rule before his death, but the Senate had to grant him the official titles that had been vacated by Augustus on his death.

I think the "Divine Right of Kings" you mention is probably tangled with modern Protestant, democratic and enlightenment notions about God being a mostly private endeavor and kings being an aberration. Chapter 10 of G.K. Chesteron's "Short History of England" touches on exactly what you want to know*.

He wrote that the supporters of the divine right of kings like Robert Filmer

... professed the impossible ideal of “non-resistance” to any national and legitimate power; though I cannot see that even that was so servile and superstitious as the more modern ideal of “non-resistance” even to a foreign and lawless power.

It's important to understand the difference that may have been apparent to people educated under the Catholic Church in the middle ages that there is a distinction between Natural Law and Human Law.

A king, despot or any other civil authority always has some degree of control over "Human Law" in any society (outside of an actual democracy by mob rule). Who then, do those leaders, whether they're elected or born into the role, gets their authority from? Some would say the people, some would say God, either way it is not "Human Law" which makes a person a ruler, it is a thing natural to man.

Locke would not agree with this, but (according to a Patriot's History of the United States) many of the founding fathers of the United States of America would . Some think government is a natural thing regardless of the form it takes, some think it is a superficial thing external to mankind. In the middle-ages, government was a natural institution.

So, depending who you ask, Divine Law is either a subset or a superset of Natural Law. The Catholic Encyclopedia clarifies it a little bit (hopefully not anachronistically)

This Catholic doctrine concerning the Divine origin of civil authority, as it is inherent in society, must be carefully distinguished from the theory of the Divine right of kings which was popular in England among the High Church party in the seventeenth century. According to the theory of Divine right the king was the Divinely constituted vicegerent of Jesus Christ on earth; he was responsible to God alone for his acts; in the name of God he governed his subjects in both spiritual and temporal matters. The theory united the spiritual and the temporal power in one subject, and derived the combined authority from the direct and immediate delegation of God. It has not ineptly been called Caesaropapism.

So that kind of Divine Right, the kind Henry VIII would have used as a pretense to drain the monasteries of England dry, would not have been the same Divine Right assumed by peasants and rulers alike in the Middle Ages, where submission to the Pope and the Church was a taken for granted.

Furthermore, Chesterton wrote:

It was not really even so simple as this; for the Middle Ages were not, as it is often the fashion to fancy, under a single and steely discipline. They were very controversial and therefore very complex; and it is easy, by isolating items whether about jus divinum or primus inter pares, to maintain that the mediaevals were almost anything; it has been seriously maintained that they were all Germans.

So, I think he's getting at what you are saying as this being a broad question, it's very broad because it means many things.

But it is true that the influence of the Church, though by no means of all the great churchmen, encouraged the sense of a sort of sacrament of government, which was meant to make the monarch terrible and therefore often made the man tyrannical. The disadvantage of such despotism is obvious enough. The precise nature of its advantage must be better understood than it is, not for its own sake so much as for the story we have now to tell.

And the advantage, if not the reason people put up with "Divine Right" might be:

The advantage of “divine right,” or irremovable legitimacy, is this; that there is a limit to the ambitions of the rich. “Roi ne puis;” the royal power, whether it was or was not the power of heaven, was in one respect like the power of heaven. It was not for sale.

Which is very much the same reason Bernie Sanders and Donald Trump have done so good recently, both substantially make the claim that their right to rule would be natural and not for sale (in this case, not for sale to banks instead of barons).

^{* Short History of England on Gutenberg and Librivox}