Monarchies in fantasy novels are a dime a dozen. They’re everywhere. You’ll sometimes encounter republics, or theocracies, or magocracies described, but usually as background nations- they may interact with the story, but they usually aren’t the main setting. One of the most common plotlines associated with monarchies is that of the usurper- the protagonist, usually the heir to the throne, must reclaim their kingdom from an usurper, who is often related to them. And, frankly, I’m a little tired of it.
Part of the appeal of monarchies in fiction for writers is the ease in which you can anthropomorphize government- The king is the government, at least to the people. You can easily establish protagonists and antagonists through the monarchy (The king is battling greedy nobles, the king is an usurper and must be overthrown, etc, etc.) It’s much harder to do this with many other forms of government. Another part of the appeal is that monarchy is simply the first system most people think of when they think of fantasy. “Oh, there’s swords and such? Must be a monarchy.” Hell, I do it. It also allows for greater focus in the plot if the antagonist is outside society- a dark lord, ravenous hordes, an all consuming plague, giant monsters, etc. With a relatively simple, easily understood governmental system, the plot can slam itself right into the external threat. Simple literary inertia plays a role, too- it’s easier just to keep going with the flow. There’s a reason Tolkeinian Elves, Dwarves, and Orcs are still so prevalent in fantasy- they’re effective tropes that the audience already understands. Same thing with monarchies.
Democratic and popular revolutions aren’t entirely absent in many novels, but they are often sideplots at best. Kristian Britain’s Green Rider series has one, but it is foiled early on in the series by the (benevolent) monarchy, and is entirely absent later.
There are a lot of reasons why monarchies are so prevalent, but what effects do monarchies have in-story? Primarily, they provide a sense of in-universe stability. Society, the kingdom: They are, in some form, immutable, held that way by the kings and queens. Monarchies usually aren’t that stable, but they’re frequently portrayed that way. They’re given millennia-long histories to show that this world is unchanging. There are swords, magic, dragons, you name it, and there always will be, because there is a stable monarchy. They won’t put up with any of this nonsensical societal change, technological development, population growth, or even linguistic drift. Even when an usurper pops up, the heroic heir, once they regain the throne, will just keep things going in the traditional manner, albeit with some tax relief, famine/plague ending, minor civil rights that really don’t amount to much, minor skin disorders cured, and a brand new war against one of their neighbors. Now back to the fields, beloved peasants!
For those of you who would like to read some fantasy that shifts away from the standard monarchic paradigm,, check out Brian McLellan’s Powder Mage series, Lawrence Watt Evans’ Bound Lands Duology (A Young Man Without Magic and Above His Proper Station). The Powder Mage books are a bit more action-packed. They’re about a military coup turned democratic revolution, with gods and magic thrown in. The Bound Lands books are… unique. The main character, rather than being some unstoppable warrior, is an orator. An underground demagogue raising public anger against the magocratic government in a fantasy land. I highly recommend both. Also, there are always the fantastic Discworld novels, by Terry Pratchett, where most of the books take place outside traditional monarchies. (Except for the Lancre books, but the monarcy of Lancre is hardly… the most, well, majestic.)