It is one of the reasons why I, too, like the TV series - when I see the Earth Kingdom, I see people I grew up with, being ordinary people, rather than strange exotic peoples. Moreover, I see them as movers and shakers of the world, rather than passive observers.
And I can cosplay Toph, or Mei, or Ty Lee, or Azula. Do you know how hard it is to find someone I can comfortably cosplay? Because most animated characters I see are either characters who I look like but cannot cosplay, or who I like but cannot cosplay without rather betraying the sense of the character.
Now, some little white girl is going to play a little Asian/Inuit girl. You cannot divorce Katara's character from her skin colour; it is part of her. It is also part of why so many little girls from minority races like her.
I ... feel sorry for M. Night's daughter. Because at the end of the day, her father didn't bother looking for a girl who looked just like his daughter to play Katara. I really don't care how "perfect" Nicola Peltz is; there are going to be little brown girls who will find their hearts somehow broken by this.
They will not have a name for it, because they are too young to understand the implications of representation on visual media.
They will not have a name for the sadness that their favourite character no longer looks like themselves, and when they try to voice it, they will be shut down as being too sensitive, and it's just a character, and they will be told they are the racist, for caring about the skin colour of the actress who plays that character they saw themselves in.
There will be some children who will feel betrayed by these changes, and the adults around them will gaslight their concerns, telling them that there's no real problem, they're just imagining that it's a big deal that suddenly Katara doesn't look like them at all.
If I had a father who was a big-name director, who could cast whoever he wanted in a role of a little girl who looked like me, and he didn't cast someone who did look like me? I would be asking, Daddy, what's wrong with me? Am I not worth portraying on-screen? Don't little girls who look like me deserve some effort in the search for the perfect actress?
M. Night is inconsistent when he speaks about the auditions for Katara, because he says elsewhere that he wanted Nicola Peltz from the start. He has never said what it is about Nicola Peltz that is exactly like the series. He has never said what drives in the resemblance. Nor has he said anything about what his daughter thinks about his choice.
I find the absence of this as telling as the continual praise for Nicola Peltz.