If Katara ended up with Zuko instead, she'd be remembered as a warrior...
..is the take that's making rounds around TikTok and Twitter currently, that I disagree with. So let's talk about that.
First of, just to get it out of the way, this is a blatantly mysogynistic thing to say. To imply that a legacy of a woman is defined not by her actions but by her man, and that the "soft" guy "softened up" her image to a weak little healer, but the "edgy, cool, bad boy" would have "let" her maintain the edgy image of a warrior.
Way to completely undermine a woman's agency and ability to control her actions and how they are remained in history. Way to water down the achievements of a woman by implying they're so insignificant that she needs the "right man" to make sure they're remembered, and the "wrong man" will let them be forgotten. Way to imply that being remembered as a healer (a "traditionally" female role in the eyes of some of the fandom, because the way the NWT operates affected how fans perceive WT culture in general) is inferior to being remembered as a warrior (a "traditionally" male role, for the same reason as above). Your internalized mysonigy and hatred of everything you associate with femininity or womanhood is showing.
But that's only a footnote I have for this take. Another reason I don't like it is because it doesn't make sense.
In order for Katara to be remained as a warrior, either her greatest achievements that everyone knows and remembers more than anyone else should be fighting-centered, or she'd need to spend the majority of her life as a warrior so she's more warrior than anything else. In both scenarios, it's unlikely Katara would have been remembered as a warrior in any scenario, simply because she's been a healer for longer than she's been a warrior, and boyfriends don't change that.
Katara was active in the battlefield for one year of her life. And then there was no more war. So in order to be remembered as a warrior, Katara would have to retire from everything forever, or do everything she does for a lesser amount of time or with lesser results/effectiveness levels, allowing "Warrior" to remain her most longlasting/successful role throughout her life. And that's simply not like Katara at all. She was never able to be passive to people needing help or support, she would want to do something. And seeing as that "something" wouldn't be "Warrior" (because there's hardly a need for a warrior without a war), she's bound to do something else, for a prologued amount of time, and that something else would ultimately be what she was remembered as, because it'd be what she did for majority of her life.
Now, that "something" could have been scientist or politicians or teacher or cleaning lady or archeologist, but it ended up being a healer. And that had nothing to do with Aang and everything to do with a fact that she's a good healer and she likes to heal. Her healing abilities and their importance have been repeatedly showcased, and Katara's willingness to help people in whatever way she can. A warrior is only needed when there's a war, but a healer is only needed every time somebody gets injured or sick and needs help. And Katara likes being able to help. So, considering she couldn't remain a warrior without a war, she became a healer because these are always needed, everywhere, at all times. And then she remained a healer for several decades, resulting to her being remembered as one. It had nothing to do with Aang, and everything to do with Katara. And dating Zuko wouldn't have changed that.
There's only one way Katara could've possibly remain a warrior after the war was over, and that would be if she joined an army of some type. And I'm sure a mix of war related trauma, plus seeing some level of corruption in most of the armed forces she's encountered, plus not being much of a flag-praising patriot, Katara wouldn't want to join any armies.
With the war being over, in order to reimain a warrior, Katara must join some type of armed force and continue war-ing.
Katara wouldn't want to do that, so that's out of the question.
Without an ongoing war or military service, the only way for Katara's main point of legacy to be her as a warrior is if Katara didn't do anything else better or for a more prolonged amount of time, allowing the label "Warrior" to keep the spotlight.
Katara wouldn't want to do that, because she doesn't want to be a passive figure in the narrative, she wants to be helpful and impactful. She wouldn't want to retire. She'd become something else.
So remaining in history as just "Warrior" is out of the question. She'll do something else, with more successfully or for longer, and that'll be her legacy.
What will that be? Maybe the skill she's been honing over and over again throughout all three seasons, the skill everyone values and needs because it's indispensable, and the skill she is proud of having and fits with her character and narrative because she likes helping people. Healing!
Flashforward to the last years of her life, Katara has been a healer for decades, she's helped countless of people, saved several lives, maybe taught her craft to somebody that was interested in learning, and her legacy is that of a healer because that's what she spent most of her life being.
You see how, in this cohesive train of thought that concludes with Katara being a healer while remaining faithful to her characterization and making sense narratively, I didn't mention Aang or Zuko once? That's because Katara being a healer had nothing to do with either of them, and everything to do with it making sense for who she is.
If she dated Zuko, would the war he everlasting so she can remain a warrior? Would she join the army to still be considered a warrior even without war? Would she retire after the war and never do anything again to let the war era define her entire legacy? No! She'd still become a healer! Because it makes sense for her character! And she'd be a damn good healer for a real long time, so she'd still be remembered as a healer!
Katara's actions are defined by HER, not any love interests. Katara's legacy is defined by HER actions, not who her husband is. Katara would still be a healer and be remembered as one no matter who she dated, and that's okay! Because she's proud to be a healer and it fits her narrative and character!
And it's misogynistic to imply her being a healer is wrong or bad or lesser than, and it's mysogynistic to imply a different boyfriend would fundamentally uproot her personality and values to the point being a healer doesn't fit her anymore when it's been part of her skillset and characterization since early book 1.