Viv is all about control, but it's not because she's power hungry like people believe. I think it's very clearly due to trauma she endured as a young mage. Of course we don't get specifics but as always, banter with Cole gives a huge insight:
Inquisitor: Cole, Vivienne doesn't want to talk right now.
Cole: She's afraid!
Cole: Everything bright, roar of anger as the demon rears. No, I will not fall. No one will ever control me again.
Cole: Flash of white as the world comes back. Shaking, hollow, Harrowed, but smiling at templars to show them I'm me.
Getting the "gift" of magic is clearly a traumatic event for a lot of mages, because they can't always control it, and when it's noticed, their entire world is turned upside down. They're taken away from their families, stripped of any rights or titles, and thrown under lock and key. We have no idea what Viv's life was like before she was a mage, or how her power manifested, but even if it was all fairly benign, it's still a traumatic experience.
Viv and Sera make a great contrast, because both experienced the loss of control that comes with being on the lower rung, but while Sera's response was to want to throw tomatoes at the system, Viv wanted to get on top of it and make it hers. They both have a rather rigid response to it, Viv pulling inwards to grab the reins and never let go, Sera getting wound up and angry and exploding outwards. They both want order and stability though, because they are both keenly aware that a lack of greater order is what causes those destabilizing situations that they're both so terrified of.
Another key thing with Viv is that she's the only one who gives approval and comments approvingly to you if you save everyone at Haven. It makes her very happy when leaders use their power efficiently to help the people beneath them. I think part of the reason Viv is so invested in the direction of the Inquisition, and mages in the Chantry is that she wants the power, not only because of her own control issues due to fear, but because she would use it responsibly and create systems that would protect people. (And she does, if you look at her Divine slides). I think for her, its a bit out of character to start rambling about the little people, because she’s spent so long manipulating Orlesian nobility and her mentality won’t allow her to fully empathize with victims (because she was one, and she transformed herself into something else so she keeps a barrier there) but there are plenty of hints that she cares, and much of her disapproval comes from when you take actions that she thinks endangers the stability of people’s lives.
What makes me so sad about Viv is how isolated she is. When she says things like "sentimentality is not an option" or "my opinion doesn't matter when there are facts", she means it. She triumphs externally at the expense of her internal world. She doesn't form close connections, and when she does (like with Bastien), there are always walls, barriers, rationalizations (he's wealthy and can help her) and she always holds herself at arms length, because she seems to knows from experience that the best way for someone to control you is for you to care about them. I do think that when you get high approval with her, Indira does a great job of ever so slightly varying her tone so that Viv doesn't sound like she's condescending to you, but it's more of a playful thing that lets you in with her on it, if not pulls you in completely. I actually really dislike that you (or anyone) couldn't reach out to Viv more, or have her form something more meaningful. I think they focused so much on her as a badass they forgot how lonely the stoic badass is inherently. I think she and hardened, unromanced Leli have a lot in common there.