What I think Noxus is like
Tl;dr I think Noxus is an extremely militaristic America.
It's made pretty clear that Noxus values strength above all else. Similar to a laissez faire free market, Noxus has embraced the ideas of as little regulation on the military sector as possible, and as a result is at the cutting edge of military excellence, weapons technology, and magical prowess. The very foundation of Noxus is the Noxian dream; It is to join in war, to kill the enemies of Noxus for honor, power, status and prosperity. The fact that any Noxian can take up arms; That even those in grinding poverty can work hard, and rise up to become a powerful and influential warrior is what makes Noxus the best damn country in Runeterra. I get the impression that Noxus believes and values the power of the individual to pursue their own destiny, and respects it. But I also get the impression that those who don't fight, are second rate citizens; Cowards who don't deserve rights, and will be used to feed those who will fight.
This is why the Noxian citizenry doesn't rebel against their seemingly tyrannical government. They don't, because they believe in what it stands for.
If the citizens didn't believe in the pursuit of power themselves, and just wanted to enjoy the safety and prosperity that the Noxian military brings, then I don't see Noxus lasting very long. Morals are the goo that hold any society together, and Noxus has immorally sacrificed these same people for the sake of these very beliefs. If they don't believe in it, then they ought to have joined in a rebellion by now. Also, there are frequent mentions of Noxian leadership's incompetence, corruption, and assassinations galore, a tell tale sign of the lack of morality that's ripping the country apart. Swain and Darius may have removed the incompetent, corrupt leaders, but they cannot unify a country alone. The citizens themselves must believe in strength for there to be any stability in Noxus.
"I came to cut off a piece of that Noxian dream... and I ain't sharing my piece!" -Kled
