Honestly the comparison of zutara to the Hades x Persephone myth feels so poignant when you remember that the original version of the myth had such a huge focus on Demeter's grief, as well as that of the nymphs who were Persephone's close friends.
Like Demeter grieves. She strips of her jewels and refuses to drink ambrosia and nectar, she wears black as if she were a mourner, and she wanders the earth in search of Persephone. But because Persephone was kidnapped by Hades, no one dares tell Demeter what happened, or where she can find her daughter. It is only Hecate who helps her and in the end, Persephone only has to return to the Underworld because she was tricked into eating three pomegranate seeds.
There is an argument to be made about how this is the more 'feminist' retelling, as it lays bare the partialchal nature of ancient greece in Hades' treatment of Persephone, Zeus' encouragement of his act, and the way the entire universe bands together to defend Hades. It does however, also show us Demeter rebelling against this status quo, despite her grief and pain fighting to save her daughter imprisonment, with the help of another woman at that. It's, essentially, a tale of older women banding together in an attempt to rescue a younger woman from being used and abused by the patriarchy. A story of solidarity and community between victims, if you want to take it that far.
I can't help but find some strange similarities between how Aang and Demeter are treated by those who wish to elevate Zuko or Hades as a potential romantic partner to Katara or Persephone.
Of course, Aang isn't Katara's mother (though there are some strong parallels between him and Kya and them sacrificing themselves to the fire nation), but the aspect of solidarity between victims is very much still maintained. Demeter and Persephone are both women in a heavily patriarchal world full of male gods who really will stick their dick where they damn well please. And Aang and Katara are two genocide survivours being hunted by the nation who went through with those genocides.
However, these incredibly important relationships of mutual love (whether familial or romantic) and support are downplayed in order to prop up Hades, a man who heavily benefitted from the misogynistic treatment of Persephone, or Zuko, a prince of the nation which caused irreparable damage to Aang and Katara's cultures and lives and supported it for a huge chunk of his life.
In fact, they are often in fact portrayed as the ones that are actually holding our heroine back.
Demeter becomes a controlling, overbearing helicopter mom. Often, winter coming around due to Persephone returning to the underworld is shown as some petty spite on Demeter's part, rarher than grief and sorrow so uncontrollable that it bleeds into the physical world.
Aang's flaws are blown out of proportion, his mistakes overly scrutinised, his positive aspects overlooked. Similarly to Demeter's winter, the Avatar state is no longer a physical manifestation of grief and pained rage, but rather a 'supernatural tantrum' that Katara has to gentle parent him out of.
There's also a significant 'blunting' of the flaws of Hades and Zuko, as well as an assumption that the heavily resisting woman just needs to get to know him. That she can tame him, and in return for her "light" he will give her a fraction of his power.
The emphasis placed on Persephone as a queen of the Underworld and 'Fire Lady Katara', on how they can improve and help realms that are entirely seperate from their domains, and have been, in Katara's case, hostile towards her, makes it feel like the empowerment these heroines recieve is due to their association with their potential romantic partner, not due to their own merit.
And, frankly, I find that a hollow type of empowerment. Call me old fashioned, but I liked it when the story was about victims loving and supporting each other and trying to overcome a world that had it out for them.
But oh well. We cant have nice things lol