@ Ghost Gal
Your Iron Bull comparison is apt, but there is one crucial difference between the two: Sera command a network of spies, whereas Bull commands a unit of mercenaries.
Obviously you want your mercenaries and your bodyguard to be at your side, and you want your spies to be elsewhere, actually spying. Sera says as much, that they wouldn't be very good spies if they weren't in the places where they can find useful information. You aren't supposed to know who Red Jenny is, hence the moniker. She hides herself even from her subordinates. They aren't going to be playing cards during their downtime.
I did concede that we don't get to see Sera interacting enough with the poor. But, I think this is generally a flaw of DAI as a whole, not just her. We don't really get the level of interaction with people that we got in Origins or even DA2 - most of the common people are there to simply hand out quests and have a line or 2 of dialogue at most. We don't get those quests that really contextualise the world, or that level of conversation with randoms that we got in Origins, such as in the Brecilian Forest, Orzammar, or Redcliffe.
As for the whole 'judge, jury, executioner' - my point was that in a feudal system, nobody is put into their position in a fair and democratic way. If the Empress of Orlais can decide who gets to be that, suiting to her own interests and prejudices, then why can't Sera decide the same on the same basis? Because she wasn't born in the Winter Palace? Neither are accountable, neither are fair, so to criticise the one outside the system yet not the system which creates the same thing seems to me to be short-sighted.
The crucial thing I want to say, though, is that Sera might not be a morally good character, but being morally good and being likeable are not the same thing. Who you like is far more subjective. There are so many different personalities and political and cultural backgrounds in DA companions that it is pretty much impossible to like and agree with everyone on everything. There will be those that you like and dislike, those you agree with and disagree with, those you can't bear, and those you couldn't play the game without. And those characters are not perfect: they have their own biases, prejudices and experiences which colour their views, just like real people.
I think Sera's greatest strength as a character is the levity she provides in a game which sometimes veers into over-seriousness. For that reason, even if I don't agree with her political views or moral stance, I still like her as a character, even if she was never the loveliest girl.
A great real world example of likeability vs morality is the WWE. Stone Cold Steve Austin was a character that was morally ambiguous at best, and amoral at worst. Yet he is, and was, universally adored by the fans. Whereas John Cena is unquestionably a morally good guy, yet he is disliked by a not insignificant portion of the fanbase.
An in game example, for me, is Anders. He was not a morally bad person. He fights for the oppressed, he heals the sick, and he fought the darkspawn. But I found him to be unbearable, preachy, and dour. I also disliked Aveline, despite her being a good person she seemed to spend a huge amount of time nagging Hawke because of this thing or that. Yet someone like Merrill, Oghren or Leliana, who were far more morally dubious, I really liked. And then you have Fenris, who is neither good nor likeable, but he's a rare example. One of my problems with DA2 was that many of the companions weren't likeable (at least in my opinion) and had personality traits better suited to antagonists than friends.