My complaint isn't that it's out of character, it's that I don't know what (if anything) the writers are trying to say, or what the message is that the viewer should take away from the episode. The plot and the antagonists weren't interesting or well-written enough IMO to give the killing any proper impact and it doesn't illuminate or alter anything about Seven's character, nor does it conclude the story in a satisfying or interesting way, so it just ultimately feels like yet more violence added for the sake of it.
Really? Because it seems fairly obvious to me.
Consider that each episode of PIC, aside from the first episode, starts with a flashback (and the first episode started with Picard’s dream of Data in Ten Forward, thematically the same thing.) This establishes that a leitmotif of this show is people being haunted by the past.
“Stardust City Rag” begins with Icheb’s extremely graphic and painful torture, something that Seven was not able to arrive in time to stop. It’s obvious from context that she and Icheb deepened their relationship upon returning to the Federation. Witnessing such a terrible crime has deeply affected Seven, and it’s the framing device for the entire episode.
In VOY, Seven was portrayed as extremely loyal to people. Her relationship with Janeway was a central feature of the show’s last four seasons. So Icheb’s fate deeply affected Seven. Add to that that the person ultimately responsible for Icheb’s death was the woman she (apparently) had a romantic relationship with. So, Seven has been deeply betrayed by her, in such a way that Seven’s loyalty was broken TWICE.
Ultimately, Seven’s story in this episode is used to show what kind of universe is out there outside the Federation, in former Romulan space. But its real effect on the audience is in our affection for the character of Seven and in showing how her story ties back to one of the ultimate themes of PIC: how broken people, haunted by their past, are driven to do desperate things.