At its root, a lot of the subgenre seems to be about the possession and distribution of power and authority, whether that is power over a family, another person, a business, a religion, a kingdom, an empire or a whole world. The clash of those people with different agendas seeking (or avoiding) power drives many works in the subgenre.
"Fear my mighty warhammer!"
"Not that mighty from this angle, actually. Oh hang on, that wasn't a euphemism?"
"Not that mighty from this angle, actually. Oh hang on, that wasn't a euphemism?"
In Tolkien's Middle-earth mythos, the clash of power takes place between the not-always-clearly-delineated forces of 'good' and 'evil', driven by the betrayal of the Valar (god) Melkor/Morgoth against Illuvatar, the creator of the universe. This clash results from Melkor's wish to control the development of the world that Illuvatar has created, Arda. That Melkor is a god with immense power over the world is not enough, he must be the ultimate force in the universe and will not rest until he achieves it. As The Silmarillion proceeds, however, Melkor is continuously diminished in power and stature, starting out being able to challenge Illuvatar himself and later being physically injured in single combat with the elven king Fingolfin. He even loses his godly name, becoming the accursed Morgoth as the book and the War of the Jewels proceeds, before losing all of his power when he is cast into the outer darkness. Morgoth's diminishment and defeat allows his protege Sauron to rise to replace him, and in an interesting contrast his power rises from that of an ordinary Maia (angelic or demonic spirit) to that of a demigod many times more powerful than his former peers, such as Gandalf and Saruman.
This leads into the action of The Lord of the Rings, where Sauron's greed for power and authority leads to his own destruction at the hands of the hobbits, beings notably not seeking such status and recognition (though they receive it anyway) in a classic tale of hubris and the mighty being undone by the meek. Where Tolkien falters is with his character of Aragorn, who seeks the throne of Gondor, vacant for over a thousand years, on the basis of his great-great-great-something-grandfather's claim despite Aragorn and his ancestors notably failing to claim the throne in the interim, which could have provided stability to the kingdom and possibly avoided the weakening of Gondor which led to its vulnerable state during the War of the Ring in the first place. The timing of Aragorn's play for the throne seems to be down to dramatic convenience more than anything else. In this regard, Peter Jackson's take that Aragorn (and presumably his ancestors) is reluctant to take the throne due to his fear of the corrupting influence of power ("The same weakness," that Isildur had) actually makes more sense.
Aragorn getting the throne of Gondor in this manner has led to accusations of Tolkien favouring authoritarianism, an accusation which has since been voiced against other fantasy authors working in the same field. Certainly this accusation would have stung Tolkien, whose loathing of Hitler and (especially) Stalin is very well-known. This criticism does expose an inherent problem in epic fantasy, namely that the typical faux-medieval settings of the subgenre tend to echo the real political make-up of that time period, which favoured strong leaders, often inheriting their power from their parents (usually the father) rather than the will of the people.
In this sense epic fantasy tends not to like to challenge the order of the day. Often this is understandable in that worker's revolutions and the enfranchisement of the masses comes from widespread education ("Libraries gave us power,") and employment ("Then work came and made us free,"), which tend to follow industrialisation. Most epic fantasies take place in pre-industrial societies (often centuries prior to industrialisation, assuming a similar development to the real world), so asking why the inhabitants of Osten Ard haven't kicked out both Joshua and Elias and set up the Worker's Revolutionary Front of Rimmersgard is a bit like asking why a popular uprising didn't unseat the Tudors in the 16th Century. The time was not yet ripe. Those secondary world fantasists that do want to engage in this question, such as China Mieville's Bas-Lag books, use an industrialised or steampunk backdrop to explain how the people get to the point of demanding social change.
Still, this leaves the problem that there are many books out there where the principle storyline seems to involve one unelected (tyrannical or benign) dictator being replaced with another, sometimes several times through the course of the narrative, usually on the questionable basis that the new king is better than the old one on the basis of just being a nice guy. Garion in Eddings's The Belgariad being a typical example, although Lyam in Feist's Magician also falls into the same category.
In this sense, Jordan's Wheel of Time is mildly different in that Rand al'Thor isn't that nice a guy as he railroads and bullies the nations of humanity into following him against the Dark One 'for the greater good', developing tyrannical tendencies along the way before being brought back from the edge in The Gathering Storm. This series is also notable for featuring somewhat proto-democratic institutions (such as the Aes Sedai and Whitecloak councils), reflecting the much more widespread nature of education and social developments in the world (the WoT world is more akin to the 17th and 18th centuries, whilst the tech level is somewhat earlier). The series also addresses other types of power and authority in the books, most notably through the controversial character of Elayne Trakand.
Elayne is the heir-apparent to the Lion Throne of Andor when the series opens, but eventually develops the ability to channel the One Power and is taken into the ranks of the Aes Sedai sisterhood. Elayne's mother, Morgase, is corrupted by Rahvin, one of the Forsaken servants of the Dark One, and neglects her duties, plunging the kingdom into corruption and risking civil war. When Morgase disappears, the Andorans expect Elayne to take her place but instead Elayne spends a few more books arsing around looking for a weather-control magical device before deigning to show up and take on her responsibilities (which seem to involve ruling the kingdom, somewhat confusingly, from her bathtub). Understandably, there is more than some resistance to this idea and a brief civil war results before Elayne is victorious and is crowned Queen. What is ridiculous about this storyline is that at no time does Elayne acknowledge the validity of the complaints voiced against her: that she neglected her duties to Andor in favour of those as an Aes Sedai. As such, it is questionable whether she can serve as Queen when her first loyalties are blatantly not to her people or kingdom, but to another institution. Jordan thankfully shows some awareness of this problem (Elayne's coronation is accepted by many of the high lords of Andor as a peace-restoring measure, but many are unhappy with her attitude), which hopefully will be addressed further in Towers of Midnight.
An altogether more comprehensive take on power and authority is undertaken in George R.R. Martin's A Song of Ice and Fire, where it is the primary theme. The Targaryen family has displaced the separate ruling dynasties of the former Seven Kingdoms to forcibly unite the kingdom at gunpoint (well, dragonpoint). When the Targaryens are destroyed and their survivors driven out of the continent, the usurper, Robert Baratheon, claims the throne through a combination of might and a blood-claim dating back several decades. Despite his initial success, the dragonless Robert is unable to hold the kingdom fully together and upon his death it splinters apart, several of the families fighting for control of the whole continent and others taking advantage of the chaos to declare independence for their regions.
Reflecting the title of the first book, A Game of Thrones, the reader is practically invited to choose a side and argue the validity of that side's cause (as they have done in person and on message boards for almost fifteen years now): do the Starks have the right idea in returning to their region's former independence from before the Targaryen invasion? Does Stannis Baratheon, as both Robert's true heir and the heir to the Targaryen family (his grandfather married King Aegon V's daughter) within Westeros, have the right of it, despite being a harsh and ruthless martinet? Or should we be siding with Daenerys Targaryen, the displaced heir to the Targaryen family line, who is marshalling her forces in the far east in preparation for her triumphant (or not) return?
More interestingly, Martin does address the role of the common people in this conflict. Whilst the People's Soviet of Oldtown hasn't appeared (yet), the smallfolk have unified under the banner of religion (in this case the Faith of the Seven) to try to stop the war and the violence, something the Faith has been more than happy to help them with (of course, because it restores the Faith to a level of power and authority it has not enjoyed in almost three centuries).
The role of religion in epic fantasy is thus something of a way of engineering change in a pre-industrial society, which makes it all the more bemusing that it is so rarely addressed in epic fantasy. There is no religion at all in Robert Jordan's world, it plays a minimal role in Raymond E. Feist's Midkemia and is even barely acknowledged in Middle-earth. It falls to Martin, to R. Scott Bakker's Prince of Nothing trilogy (where a man engineers his own recognition as the messiah to seize ultimate power), to Paul Kearney's Monarchies of God sequence and to Kate Elliott's Crown of Stars series to address the matter of religion and how it promotes or abuses its power in a pre-industrial society.
Returning to the original point, the changing role of power and authority is a primary driving force of epic fantasy, but the genre's typical settings seem to limit how radical those changes can be, mostly resulting in the person in the chair changing but not the corrupting influence of power that led to problems in the first place (though this observation itself is sometimes the point, as in Martin's series). With the increasing popularity of non-medieval settings and steampunk and industrial fantasy settings, there is an opportunity here to see more flexibility and originality when it comes to the role of power and authority in fantasy.