If Suki decided to join the Gaang on their trip North, it wouldn’t result in a love triangle. No, it would be Suki and Sokka just standing there like:
Wow...pretty princess! Pretty princess with hair like snow! Love us pretty princess!
Then Zhao wouldn’t even get close to that pond because Suki is there and Suki is Suki
So maybe Yue joins them, but I think instead it’d still be a super sad goodbye since they know the one heir of this kingdom can’t go on a life threatening adventure. So it’s these two being like, hey I hope we make it! If we do and you’re still down we’ll come back and fight whoever your dad tries to set you up with.
(And because I’m polyshipping trash) this goofs would return months later with Zuko like:
Hey Yue, we still love you but also apparently our type is pretty royals so we did pick up a stray. Hopefully we guessed correctly in that your type is people who are both dangerous and awkward.
Yue would be like hot damn Christmas has come early and my dad can’t even say no because how can he turn down the fire lord (as well as the Avatar’s battle strategist and the leader of the kyoshi warriors).