@icekatze, I don't know what to tell you, please don't force yourself to read something you don't enjoy. The below isn't an argument to keep you reading, it's just the way I see things.
Chapter 2 establishes Menou knows she is the monster here and feels the weight of killing school children in her dreams. It also further establishes she used to be a pleasant person before something happened, if Momo is to be believed.
Chapter 4 heavily implies that the "something happened" was a town being obliterated by an otherworlder. Back to Chapter 2 implies that may not have even been the otherworlder's intent and is just known to be an inevitable fate for all otherworlders. Since there are 4 novels out and we're still in the first, something may not quite be right with that 'knowledge'.
Chapter 8 reminds that saving people is her first priority and the only reason she became an Executioner was to prevent a recurrence of whatever happened "that day". She didn't even kill the terrorists because it seems the only people she's willing to kill are the individuals trying to bring innocent walking nukes into their world. I'm not even sure she was faking it about not wanting to subject Akari to pain; I think to save the passengers she would do most anything, so my bet is on it being calculated, but it could have been sincere.
Akari is clearly an airhead to some degree, but only one guy was shot in the foot and then Menou protected her with ease: What does she have to worry about here? She's going from a world that she says she didn't really want to go back to in Chapter 3, to a world where some pretty girl has come to rescue the princess and has thus far handled every situation for her. If I were on a train and the power source died, my (incorrect) assumption would also be the train would slow to a halt. The situation, to her, has been resolved with the only casualties being the terrorists (of their own volition).
As I see it, you're meant to root for some outcome where Akari isn't walking cheerfully to her death.