Their society is based on military necessity -- actually much like the very, very early Romans. When Rome was a city state, surrounded by hostile enemies, they had a much more rigid social structure.
Precisely.

Okay, this is information that has been largely lost to Aleran history (and therefore doesn't show up much in the books) but I figure you guys might like it.

When the original Roman legion arrived in what is now Alera they basically dropped into a hot LZ. There were multiple sentient species vying for dominance of the land and a strong presence of what would come to be called "feral" furies.
There were not many Romans, and a whole LOT of other races, so they did what Rome was really good at: Divide and conquer. They survived by becoming, as a society, a military machine that left the rigidity and brutality of Sparta eating their dust. They really became more of a death-cult, as a /nation/, than anything else.
There were relatively few women with the Legion when it came through, and it was immediately recognized that without them, there would be no chance at all for survival as a race. (And their enemies saw them as an obvious weakness to attack and exploit.) As a result, women wound up becoming subject to some truly insane levels of cloistered security, a legacy which has been mostly forgotten by history, but which is visible in several pieces of Aleran culture where women are still often held to second-class-citizen status because of those ghostly old security measures. You can also see it in the custom of mandatory military service for the men and mandatory civil/military service for unmarried women. When the Romans first got there, women were not given a choice about whether or not they would have children. Without enough children, the Romans were doomed. And if a woman didn't have a husband, well then. Off to the Legion camp with you. There are plenty of legionaries who will be happy to solve this particular problem.
In any case, it took them about a thousand years to overcome their most immediate neighbors and develop furycraft, and that whole time their society as a whole was held together by (perhaps justified) paranoia and xenophobia against inhuman beings who wanted to destroy them.
(Fear of the Other is /great/ at forging a cohesive and rigid society. You can forget your quarrel with your neighbor right quick when a gang of a dozen shambling hulks that look vaguely like bipedal elephants come charging down on your farms.)
In any case, that extremely militant mindset was a necessary survival tool. For the outrageously outnumbered early Alerans, might /literally/ made right. Whatever got the job done was the morally necessary thing to do. And those guys... I mean damn. They were some psychotic, cold, calculating SOBs.
Well, once the major enemies were taken care of, suddenly the force that held their society together disappeared. And, as can often happen when mutual enemies go away, the enemy of your enemy mutates back into your enemy again. Civil war ensued. Entire cities were put to the sword and torch. It was gruesome on a scale our world has rarely seen.
Until the original Gaius Primus entered the fray, killed everyone who challenged him, and forged Alera into an early version of what we see in the books. Over the next thousand years or so, Alera battled newcomers to Carna, made lots of fun new enemies, and further developed furycraft to a degree where they had a serious qualitative advantage over their foes. Once /that/ was done, their society began to relax a bit. It moved from a military monarchy to an aristocratic Republic. But the guiding principles of "protect the women" and "might makes right" were bedrock to how that society developed.
While that was going on, the aristocracy--the Citizens--realized that there were a lot more people with modest talent than there were with serious crafting skills. And, as aristocracies have done over and over again in history, they set out to make sure that they would keep their power. To some degree, that was probably the most practical way to do it. When one man literally has the power of ten thousand, if matters devolve into violence, that man is going to tend to come out on top in any case. Why make him kill ten thousand freemen to prove his point?
In any case, innovation and exploration of furycraft and its applications was strongly discouraged. The Citizenry really liked being the only ones with the powers of demigods, and they didn't want the freemen working out ways to make dinky furycraft as dangerous as the rarer talents of the Citizenry. Besides. Everyone knew that furycraft had reached its absolute pinnacle, trumping all other forms of power--military, economic, you name it. Why improve upon it when it was already the supreme power in the world?
The Academy system put the nails in the coffin of innovation, too. The most capable crafters of the realm were all being trained to think of furycraft in the same terms, with the same set of preconceived assumptions. Oh, sure, there was progress--but it was mostly very sedate, very polite and orderly progress which did not make the aristocracy nervous.
Plus, as more of Alera was settled and the number of unclaimed furies dwindled, it became more and more difficult to change social strata. The Citizenry already /had/ all the really powerful furies, and it wasn't like you could just go out and find one of your own, even if you had a natural gift. It locked them into stasis, or something that changed so slowly that it looked like stasis--which is exactly what the Citizens wanted.
Civil wars came along every other generation or so, but they tended to be brief, explosive clashes that were resolved with ridiculous amounts of carnage and unleashed furycraft, generally won by whoever had the stronger crafters. Rapid transit of information and rapid military transportation (the causeways) meant that the First Lord could jump on almost any rebellion before it could take root. Word would come back of a buildup of force, flown in by a Cursor, and legions would be dispatched immediately, covering between 200 and 300 miles in every day of marching on the causeways. Civil wars never became protracted affairs that necessitated innovation.
Um... think of it as the late medieval/early renaissance civil wars in England. There wasn't a lot of innovation going on for quite a while, there. Everyone knew that they had the finest military bodies available. Battles became almost formalized, because everyone knew the steps of the tactical dance so well. There are records of battles which were won because one captain had managed to put a gentle wind at his back, and positioned his archers with such precision that the enemy was withing range of his own shooters, while the hostile arrows fell three feet short of the toes of the first rank of troops. Fuedal Japan had a similar situation.
Oh, eventually circumstances and technology forced both societies to innovate and adapt--but those stasis periods were definitely present, and heartily encouraged by those in power.