This is one of my favorite scenes from Voyager. I have always liked Captain Janeway, and Kate Mulgrew did a fantastic job with the character, even though it was inconsistently written from time to time.
Voyager's writers always touched on the "family" aspect of the crew from time to time, but never really ran with it as much as I wish they would have due to the singular episodic nature of the show. I think that if Voyager were to be written today we'd see more arcs and more of this family dynamic, such as Year of Hell kind of alluded to.
We need a Voyager reboot immediately!
They could easily have been more arc focused and less episodic originally. As whay you are describing is what many thought it should be like, a greater sense of family etc...
Of course different people expect different things, but 70 years from home with the very real possibility that you may never get back you would expect certain things to happen. For me aside from the odd time you never really got the impression from the characters that they might never see home. Sure every year they mamanged to shave years off the journey but who is to tsay the next year would be the same.
I'm not saying they should be pessimistic, rather realestic. It sometimes as if the writers knew they would get home in the finalé but forgot the characters didn't know that.