Disagree with you on all points.
a) The city state you're allied with is not an extension of your empire, but it is your friend and partner. If it is attacked by an agressor (and all the other AI civs are agressors if they attack a CS, since CS's aren't expansionist warmongers), you have a right, and an expectation by that CS, to help defend them. You don't just yawn and let your friends get rolled over by any agressor civ that wanders by, for any kind of lame-arsed Mussolini reasons. To defend them in this situation is a completely just thing to do.
b) Selfish AI 'reasons' for attacking a CS: It's in the way of their expansion? And that expansion is more 'just' than your right to defend your friend from being destroyed in the name of selfish AI expansionism? Some kind of moral system you go by, there. Maybe it holds some important resources the agressor civ wants? Maybe the agressor just sees 'some profit in it'? Haha. And you're accusing the PLAYER of imperialism by defending them? <shakes head> If the AI wants to outbid me for their friendship, or even buy them out (Austria), so be it. But if they want to brutally conquer a friend who is under my protection, I have every right and even a duty to stop them. End of story.
The concept of "war" is tricky since it has changed over time.
In modern times, a war declaration is a big deal and it is unlikely to happen over a city state. Can you imagine the U.S. (or other country) actually declaring war on Russia after its aggression towards Chechnya or over China's treatment of Tibet? You might see plenty of denouncements, but outright war?
Alternatively, while Russia might grumble about growing U.S./E.U. influence over Eastern European FSR's and the U.S. might be alarmed that China is outspending them in influence in Africa and Asia, world sentiment would not be very favorable towards a declaration of war on such grounds.
As a result, I think it's understandable that the AI's would not consider a DoW due to city state treatment (even aggression) to necessarily be justifiable.
Some rarer examples may be Taiwan, which the U.S. has essentially "Pledged to Protect." There is a larger chance (though certainly not guaranteed) of war between the U.S. and China if China were to attack Taiwan. Or if you look at World War I, it started after an arguably justified attack on a city state. If a city state randomly killed one of my Great People units, then I'd be pissed. Russia declared war partly due to Austrian attacking the "city state" of Serbia. The U.K. got involved largely because of the invasion of the "city state" Belgium (Germany needed to go through Belgium to get to France).
And if you think we treat the city-states like property, we're nothing compared to the AI. In my last game Atilla had conquered Valletta(which led to the world basically hating him) Spain took it back but did not liberate it. I liberated it, Spain had enough Tercios to re-take it(It only had like 19 defense at this point) and then I re-took it again. I ended up with like 270-something influence because I liberated them twice. What happens next? Ethiopia gets on me about Valletta being in their "sphere of influence". He had done literally squat for them all game long and treats them like they're his. The AI complains at you all the time for buying CS that they haven't touched the entire game, claiming its "their" city-state.
In Civ V, spheres of influence seem predominantly geographically based.
Analogies might be the historical U.S. sphere of influence over Central/South America. Even though the U.S. doesn't have good relations with the "city state" of Cuba, I can still see them sending a similar diplomatic message for European/Asian countries that get too friendly with Cuba (or Mexico or Panama). In recent years, China has been looking outward more towards Asia as its sphere of influence, so it is more commonly sending similar diplomatic messages to the U.S. (even though the U.S. has maintained CS alliances with some of those city states for quite some time).
-----------------------------------------------------
The more I think about it, I really do think the Civ V diplomatic system actually mirrors real world international politics rather well. Even a lot of the "flaws" that people complain about are often flaws that exist within the existing political system itself.