The story of Hama isn't about a "native" woman breaking free of oppression, it's a cautionary tale that war can turn anyone into a monster.
Hama was not redeemable, full stop, she chose to hold onto her trauma, to not use it to better herself but to fester and become worse, to use her trauma as a justification for committing the same atrocious actions she was subjected to.
Hama wanted retribution alright, but retribution is not always a good thing, especially when you target those who had nothing to do with the injustice you suffered.
She targeted families, children, the elderly, anyone who shared an ethnicity with the soldiers who imprisoned her, and she's most likely been doing it for decades, well before Team Avatar showed up.
Who knows how many innocents she's killed in the name of her so called revenge, how many lives and families she's destroyed because she chose hate.
She never targeted Military installations, she never used her blood bending for good, she could've turned the tide of the war decades ago, but she chose petty revenge, and was intoxicated by how it made her feel like she held power.
She was a mirror of what Katara could have become if she allowed her hatred for the Fire Nation to consume her, a warning, that's her purpose narratively.
The reason ATLA is so good, is because it writes adult and realistic stories, with good messages, and isn't a vehicle for the catharsis of petty activists.
Also, Katara did connect to others of her tribe that were affected by the war, she did it throughout the entire length of the show, from the Southern Water Tribe to her family fighting on the front lines.
Every single person from the Water Tribe Katara meets understands her pain, they've all lost someone in this war, even then, she connects to many not in her Tribe, many from other tribes who she's inspired or made friends with.
She is not a character lacking connections, but she was a character, who if she didn't see what Hama became due to her hatred, may have taken the same path, as we saw in the episode where she confronts the man who killed her mother.
She could've easily killed him, it would've been very cathartic for her, but, revenge is not the story of ATLA, it's change, it's healing, and Hama plays as an amazing warning shot across the bow for Katara.
The same goes for Aang, he could slaughter Fire Nation soldiers, and he'd be justified, they killed his entire people, and his beloved mentor, but that is not the message the story wants to or should convey.
