I think the main reason for me that Katara’s legacy as a healer is so unsatisfying isn’t because healing isn’t a valuable or interesting skill, but that it puts Katara in a position of service rather than one of power, and her arc is all about her gaining power and learning about the responsibilities that come with it. Her greatest ambition was always to be strong and fearless and a warrior, as we see in the Southern Raiders when she reveals her guilt to Zuko about not being able to stop her mother's murder, and we see her grappling with how to use her newfound power a lot in season 3, when she explores both the dark and light sides of waterbending through bloodbending and through helping people as the painted lady. This implication of her becoming an accessory or auxiliary character by becoming a healer could also have been easily avoided in canon if the creators bothered to tie Katara's healing to some form of leadership (like founding a hospital in the South Pole or becoming a healing teacher, for example) but instead in every adaptation they chose to have her most profound contribution to be healing another character, usually Aang (after he makes a mistake that puts her in danger).
This is also the reason why I find it strange when people (usually kataangers) insist that zutarians and Katara stans are somehow sexist for not valuing her work as a healer. We aren't saying that healing or more traditionally female work/roles are inherently unsatisfying, but that it is unsatisfying for a narrative to shoehorn a female character into that type of work when she canonically wants to use her skills for something else. Katara explicitly states that she wants to fight, not heal, and her character arc is centered around gaining power over others through fighting back against the systems that have led to the oppression of her people and women within her culture. Katara is also something of a power fantasy for young girls tired of being relegated to "women's work", which is why so many women can relate to her. Of course people are upset with her being defined as a love interest, mother, and healer in the final season of atla and subsequent adaptations of the show. It goes against everything the young feminists watching her battle Master Pakku, show mercy to Yon Rha, and defeat Azula loved about her character in the first place. (and it's also the reason many fans envision her as fire lady or southern water tribe ambassador or at the very least a founder of her own bending school)
