What do you think would happen if Zhao was stopped from killing Tui? Yue would probably stay in the NWT and marry Hahn like you said, but again Sokka would probably try to persuade her to stay with him. He probably wouldn’t be able to convince her enough, but if he did, what do you think would happen?
I'm gonna be real with you: I think it would be very boring and unsatisfying. I think a lot of other people think so too, because every time I see a "Yue leaves the North Pole" concept, unless it's like a conflict-free modern au, Yue's character is altered from how she's shown in canon. They make her more adventurous, or more of a romantic, because as she is, she doesn't add much to the group dynamic. If the show was paced more like Game of Thrones or Harlots, more based in smaller scale machinations, more following characters' introspection, then maybe there would be something to work with. But in something so action-heavy (and I think we sometimes forget just how action heavy it is due to how often lots of action means just okay writing), a character with no interest or skill in combat doesn't mesh well long-term.
From a writer pov, Yue joining the group as it's shown to be in canon is pretty inefficient storytelling. There's nothing she could really bring with her canon personality and back story that isn't already there with Aang's connection to the Spirit World as the Avatar or Toph coming from a wealthy family. Not to mention that with her being the oldest of the group (Sokka is 15 during the events of the series, while Yue is introduced as being 16 years old, making her about a year older than him) any of the "innocence of the world" that people would wanna play with would have her come off as a bit ditzy when actual 12-year-olds in the group are shown to be more streetwise and worldly. Yue isn't a bad or poorly written character, in fact I think she's one of the most interesting minor characters in the entire franchise, but she wasn't written with the intention of being part of Team Avatar so it's no wonder she doesn't fit well among them.
So, yeah, I don't know because I don't care enough about this concept to give it any thought. An AU where Yue is sent to study statecraft or philosophy or similar topics under King Bumi's tutelage or where she has post-war peace talks with Mai representing the Fire Nation or where she goes on her own journey separately from the group with her own entourage, running into familiar faces and keeping a log of her experiences; it would be a lot more contrived, but the quieter, gentler, more introspective atmosphere it would allow would suit her much better than her staying put while the others fight their way through active war zones and bring her along.