I hate multi-quote answer fests so I'll just answer simply without individually attempting to correct your each and every statement because thats pointless and I'm not here to change your mind.
Just about any of the companions could be accused of having a broader understanding of the world they're living in than Sera. Sera rejects anything she doesn't agree with outright as unimportant. Anything that doesn't fit her little cockeyed world view as irrelevant and anything that is of no benefit to her as useless.
So she's just like you? You can take this personally, or be offended if you like, but really, you're exhibiting the exact same behavior here that you're accusing her of. What's that really say?
However, while Varric may have a similar perspective, Cass gets slapped down for her "common people" comment in party banter. Showing that some of the companions really don't have a perspective for what it's like to be at the bottom looking up.
Bringing up the war table missions that give the Inquisition benefits as some kind of evidence that shes selfless is kind of funny as her own dialogue, in many situations, indicates that she doesn't give a flip what the Inquisition achieves as long as she gets her bit off the top.
So what "bit off the top" is she getting? Varric gets an amulet that gives him an additional Skill Point after just about every mission he gets done on the Table. My take on her perspective is that she wants the scary stuff done, so she can go back to what she was doing before the world went crazy. That seems very much like a perspective that's shared by everyone there.
She is, obviously, at her best with people that romance her, and she obviously works well for people that are willing to try, so shes written as a character that makes sense to some personalities and doesn't to others.
I agree. She's going to rub some people wrong, and for varying reasons. Some are going to see a bit too much of themselves in her, and be offended. Others are going to be totally lost trying to figure out where she's coming from. Others are going to "get her", romanced or not, because they can relate to what it's like to be outside looking in, as it were.
Far as the difference between people being treated fairly and my hat at the next salon, I don't get what you're referring to. Sera uses the excuse of ensuring equal treatment to benefit herself. She doesn't care about the little people any more than she cares about the big hats...she just wants to come out on top no matter what. To take an analogous example, it would be like if Anonymous took down every big bank in America and reset the credit records of everyone in the world....then after having wrecked the entire world economy, sat there attempting to tell people that it was just fine that they took a few billion dollars for themselves because at least they were helping out the 99%.
That's the problem, because that's her whole outlook on it. She's sitting there with a low end PC, trying to play the game, having people tell her that she needs to get a console, or a new gaming rig, when she'd love nothing better, but really just can't. She's almost literally the "one legged lady at the droid kicking contest", and she rebels against that. Again, show me what benefits her, directly.
The Inquisition marches some troops through town, and gains, but there's no note that says "Sera gains 200 gold". Her benefit there is that the people being trampled in the middle of the land dispute aren't being trampled any more.
The Inquisition drops some supplies, and the Inquisition profits. She brought things to the table, quite literally in this case, that she promised, servants that don't know crap about the intrigues involved, but know bad people, and she points them out. This is, after all, exactly what she promised to do, and she lives up to it.
Even the "Noble" that she kills, if you let her, is far more guilty of "wrongdoing" than she'll ever be. You believe otherwise? Then why is it that, when he realizes that people that can fight back are involved, he suddenly wants to talk? This is exactly the kind of people she guns for, and personally, no big loss there. She's not altruistic, and makes no claim to be. The recruitment dialog is rather clear about that with, roughly paraphrased, "... and someone gets paid". Here's the kicker though, there's a very real possibility that she's not the one that's getting paid.
You are correct though. There's no real point to arguing about it. I'm not going to change your perspective, and I'm certainly not going to change mine.