It is often said that power corrupts, and due the most basic instincts in human nature, which is to survive, there is some merit to that statement. Knowing this, it might be a bit overwhelming to grow accustom to that kind of status; to almost sidestep the possibly of corruption in nobility, out sprouted the phrase "noblesse oblige". This phrase isn't so much of a law, but rather a responsibility for people in power to behave honorably and be looked up to by the people they rule over.
And to those who can't uphold this type of obligation to their people, they shouldn't be able to call themselves nobles, simply on the basis that they are in no ways noble-like. However, there are very many cases where this sense of responsibility never get upheld and a majority of those who hold the power end up ruling over their people with both an iron fist and a greedy mind. The struggle of doing what is right -- because you believe it to be moral -- versus what your peers say becomes an interesting type of conflict in storytelling, which translates well into anime.
So jumping in, I can name a few anime that display these types of ideas. However, the ones I want to focus more on are Freezing Vibration, which is of this season, and Pumpkin Scissors -- which bases a good amount of its plot on noblesse oblige, but doesn't say name it specifically.
Sea of Corruption
During the fifth episode into Freezing Vibration, Elizabeth introduced -- quite explicitly -- this topic of noblesse oblige. Because she found out that the organization she is with, Chevalier, is doing some inhumane things to E-Pandora and lying to the public. So with the power that Elizabeth had -- her family the Mably -- she wanted stand up for the people who lacked the ability to fight back by exposing the atrocities that Chevalier was practicing. She was trying to practice noblesse oblige just like her father had taught her, but the corruption and power that Chevalier has swiftly put a stop to this leaking of information -- as well as silencing their dissent by ruining the Mably name and severely punishing, most just torturing, Elizabeth.
A very similar case happens in Pumpkin Scissors as well; because the war is in ceasefire, there is some effort to supply war relief to those civilians affected. That unstable nature of everything make many people less trusting of one another -- specifically to the military and nobles. So if anything, it is up to nobility and the militia to earn back that trust, but there really was only a handful of nobles willing to do so. And in the military only one section, Army State Section III aka Pumpkin Scissors, that is specifically for war relief -- and Alice, who is a noble, was second in command for this sector.
So even if there are a handful of nobles practicing this philosophy, it isn't that helpful if you are swimming in a sea of corruption from the other nobles. And this is why there is such a thing in the first place, if the people in power aren't holding any kind of responsibility toward its people, there should be a rise to overthrow them. And if they are respectful to their people, it is obvious that no one will revolt and the quality of everyone's life will increase.
For the People
Of course with the rampant cases of power corrupting people, it is almost obvious to say that being selfish is human nature -- and there is some truth to that. That nature doesn't have to control you wholeheartedly, which is why so many people make different laws, philosophies, religions -- you name it -- to control those urges. On the surface it is to contain human nature to form some kind of well structured and functional society. And just because you are at the top, doesn't mean you are above your own human nature. So you need something that will keep you in check if you feel like you deviating from you vision.
It doesn't have to be so called "objective", or even complex, just a list of things you -- or a group of people -- feel that everyone might want to be treated like and branch from there. And that is probably one of the things that noblesse oblige tries to accomplish, even if not that many people are willing to follow it.