In short, she takes lines from many different characters who collectively could or should have been able to pick up the slack if she were never there. I wouldn't say just the Doctor and Tuvok, but also Harry, B'Elanna, and Chakotay.
I don't think she was useless or shouldn't have been there, but as you allude to, the building blocks for all of her personality traits were present among all these characters, if some different decisions had been made up front in the course of the series. By the time she was introduced mid-way through the series, the horse was already out of the barn, however, so you needed a new character introduced - or have some characters do complete reversals in their behavior.
In particular -
Seven seems like what I imagine a Vulcan child would be like - possessing a high affinity for order, structure, and logic, but emotionally suppressed and immature, without the life experience to recognize when her logic is clouded by emotion. She rebels against authority as a way to test her boundaries and discover for herself how she fits as an individual into the world around her.
As such, she possesses a few core behavioral traits that are used repeatedly by the writers -
- Arrogance that she knows better than anyone else the right thing to do
- A suppression of emotion (in her case, by necessity where Vulcans practice it by choice)
- A willingness to openly flout the command structure.
- Easily manipulated on an emotional level.
- A student of, rather than a member of, human sociological tendencies and norms.
Some of these have overlap with Tuvok and Doc. Obviously, the emotional suppression is shared with Tuvok, as is being a commentator (along with Neelix) on human social structure. I would say that in contrast to Tuvok and the Doctor, who should already have an understanding of the more complex aspects of humanity, Seven's journey is just beginning. She was assimilated as a young child, so that's really the frame of reference she's coming from when analyzing human society as an individual.
I think Harry should have been the emotionally manipulated one - as the most junior member of the crew, he should have the least life experience, and if the writers had done that, it would have been a bit more palatable that the guy didn't get promoted in seven years. He could also have been Janeway's "problem teenager."
Neelix should have been the one to be naive about humanity. He should have tried hard, but had difficulty figuring out the basics of how humanity operates - and consequently had a difficult time forming social bonds with the crew, instead of just becoming basically cook and ship's counselor by episode 3 (OK, I kid to some degree there, but not by much.) Nobody really likes him much as a friend, but they NEED him because he's a local who knows more about what's out there than they do.
There's plenty of time over the course of the series for him to assimilate into the crew and become what he became, but like so many characters it was too soon, too fast. I like Voyager, I really do, but I think that was a general problem with the start of the series. Tensions and problems between the crew should have slowly simmered, built up to a head, then been resolved over the course of seasons, were resolved within a few episodes, which shortly turned it into TNG because once they resolved those issues, they didn't give themselves the opportunity to build a truly different kind of Trek show the way DS9 did.
The role of anti-authoritarian should have been Chakotay's. I'd have liked to see Janeway keep him at arm's length for a lot longer. From her perspective, he is a terrorist traitor and not to be trusted, regardless of whether he used to be in Starfleet. He should have been challenging her every decision - standing up for his Maquis crew, and treating himself less as a first officer and more like their representative. It would be an open secret among the crew that the two of them don't particularly care for one another, but there isn't whole lot of choice, so they need to "make the best of it."
It could have been a wonderfully contentious relationship that eventually comes to a head when the Maquis crew nearly split from Voyager, before realizing just how interdependent they had managed to become.
(Apologies for writing a book. If you made it this far, thanks!

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