One thing you seldom see variety in fantasy kingdoms is in the royal succession. Nevermind the preeminence of kingdoms in fantasy, they all practice primogeniture. Nice, neat, orderly succession by primogeniture, at that. Which, in real life, is generally a sign of a constitutional monarchy where the nominal sovereign is a figurehead. The writers do have a point in that more complex succession can complicate stories. If that's not what the story is about, it can cause it to lose focus. OTOH, succession issues not only offer possibilities, they make a good backdrop of chaos.
For one thing -- are the laws of succession known? A lot of kingdoms have been ruled by customary law. The king succeeds because no one remembers a time when succession went otherwise. But when a king claims that this one or that one is just a happenstance -- or worse, all the usual stuff is not possible, for one reason or another -- trouble ensues. What do you do when no one remembers a time when a king had a living daughter but no living son? And let's not go into what happens when two kingdoms with different laws get joined. . . .
Then, there's a requirement for equal marriages in a good number of places that practiced this. The dynasts must marry someone from a royal or reigning house for the children to be eligible. Casts quite a damper on love matches if the woman is a commoner and the marriage would have to be morganatic. Great Britain never had any such requirements, but Queen Victoria rather shocked her German cousins by her willingness to let her descendents marry the offspring of morganatic marriages. (And even worse when she consented to her daughter's marriage to a subject.)
Would be even worse if you were trying to keep a royal line alive in secret. Trying to wrangle all those marriages over all those generations. . . . Russian imperial succession had a requirement for equal marriages. It also allowed for female succession after the total extinction of all male dynasts. Such have been the vicissitudes of the Russian Imperial House that people seriously put forth that such extinction has occurred and a woman is entitled to the Imperial throne.
Not that this still doesn't make life simpler than other techniques. There is the technique when the king selects the heir. If the process to select is long and convoluted, the king may not dot all the i's. If it's simple, someone can fake it. And if the king just doesn't - Peter the Great lay down the law that the Tsar chose his successor, and then he didn't. His wife ended up on the throne, such was the confusion. In China, the Empress Wu had a great deal of authority after her husband died because he did not properly select his heir; she went through two puppet child-kings before she, too, usurped the throne and ruled in her own right. And in polygamous societies, the competition of wives could be fierce; Bathsheba went to a great deal of trouble to get Solomon on the throne. (For one thing, the position of power in such societies was not queen-consort but queen-mother.)
Then there's election. Especially prone to chaos if the field of candidates was wide open and the electors not well defined. In Rome anyone could be emperor, if he got enough support from the Senate, the army, or the people, in some combination. So -- a great many someones tried. The dynasties of the Byzantium helped stabilize that part of the empire. In Scandinavia, when the kingdoms were small, the king's sons (including those from concubines) were brought before the freeholders, who "hailed" one, but as the kingdoms grew larger, such a gathering would have been impractical -- if the nobles, even, would stand it. They ended up preserving the hailing as a formality -- though it might be interesting, a story where one day, they refused. Ethiopia had a rule that everyone in the dynasty was eligible for selection; . The Holy Roman Empire may have been none of those three things, but the Electors were well-defined, and the pool of candidates small; it managed to last. Still, periods between emperors could be uncomfortably long.
And then there's coronation.
Even in history, the coronation has been held to confer a mystical privilege. One technique Roman emperors used to try to control succession was to crown junior emperors, who had no power but succeeded in the seniority of their crowning. Of course, that meant if you wanted to get one out of the succession, you pretty much had to kill him. Various Holy Roman Emperors had their sons crowned, to encourage their election. King Henry II tried to copy this; it did not work well; the Young King revolted.
And this without the magical possibilities in fantasy.
Lots of possibilities in succession. Seriously underused.