That would make perfect sense. Kim should have been introduced to, say, Lt. Seaborn, who would greet him in a friendly fashion and ask if he wanted to man the ops station for Voyager's departure while he attends to some last minute work in sickbay. Harry agrees, and Seaborn's broken corpse is later found amongst all the dead medical staff.
On the other hand, we never saw the corpse of the Chief Engineer, and never learned his, her or its name. Nor did we meet the engine boss in an introductory scene before the mayhem. So it's a pretty good match of the treatment Kim got, only without the part where some later main character would get a stint at Engineering right before the Caretaker beam hits.
Perhaps we should think that most of Janeway's crew (or indeed all of it, save Tuvok) was brand new, and nobody really knew each other, and didn't really care? There no doubt was a big funeral at some point, since the corpses should still be there unless the Caretaker somehow took care of them. It just wasn't worth showing to the audience - and not worth discussing between the characters afterwards!
But, there would have been more to it than that. Suddenly, Harry is thrust from second in command of ops to head of ops, hence his status as senior officer. But there should have been some difficulty, a period of adjustment, like if you took a third grader and stuck him in an algebra class. It's not that he's unintelligent or incapable, he's just supposed to go through all these other levels of math before he attacks algebra. Harry has to hit the ground running and try to survive. In short, we get the same character development as Nog, Jake, or Bashir, but with a new spin: the Academy grad who is just in over his head.
Perhaps so. But
every main character is suddenly a department head, and only Torres with her Klingon (lack of) patience has any trouble coping. Paris takes it in the stride, the EMH seems born to lead despite the truth explicitly being the very opposite, and there appears to be no problem relating to Janeway losing her sciences chief (or, indeed, the whole department) and doing all the work herself or with Torres.
Quite possibly Kim would be exceptionally well equipped to cope, not having spent a full day at
not being the king of the world. He studied being a heroic commander, he immediately is a heroic commander, he doesn't see anything wrong with it. Oh, some underlings may be difficult, but they're Maquis scum so that's only to be expected...
Timo Saloniemi