As for not being able to change the appearance of the origin characters, I'm not sure why that's an issue. In general, I accept it, but I don't necessarily understand it. I can't help but think there must be a reason.
Well, i dont want to call Larian lazy ... even tho that is one way to put it in single word ...
But if i would have to guess, i would bet that our Companions were modeled whole ...
Unlike our Tav, who is just set of varieties that can be put together in any order ...
In other words ... there is no Shadowheart Face, Shadowheart Hair, Shadowheart body, Shadowheart i dunno eyes ... there is only Shadowheart ... and that model (whole model) is lookig just as we see it.
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I honestly didnt even know that Mirror dont work on them, never tryed it ...
I just recently seen Wyll in some video with long dreadlooks and it looked great ... so i thought changing their hairstyle appearance would be at least one way to fresh my 85th playtrough.

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I assume what OP really wants is a customizable party...
Well ... yes, but not in this case.
Maybe try to read/listen what people say, when they talk about what they want, rather than just asume?
Its usualy working, you can thrust me ... i tryed.

If you're going to simply throw that away, then you don't want to play an origin character - you want a character who's story you write *completely*.
Im glad someone came here to tell me what i want ...
After all, its your head so how could i know, right? -_-
Seriously people ...
You dont like it > you dont do it ...
Nobody asked for moralyzing ... -_-
And even more to the point you are wrong:
which is tightly coupled to their class and identity
No ... its not and that is the most funny part.
What is part of their story?
> Shadowheart worships Shar ... thats it ... is there anywhere in forgotten realms lore said that Rogue cant worship shar?
(Hint: No, it isnt ... quite the oposite, its clearly stated multiple times that Atheists practicaly dont exists in this setting, bcs people KNOW that deities are real.)
> Wyll made a pact with Devil ... thats it ... is there anywhere in forgotten realms lore said that Paladin cant have signed pact with a Devil?
(Hint: No, it isnt ... quite the oposite, its clearly stated right in THIS VERY GAME that "paladins" who were after Karlach had signed pact with Zariel.)
> Astarion ... well ... i would like to hear any arguments that makes him Rogue, bcs this bastard is clearly a Bard.
> Karlach have anger isues and some weird machine that keeps her alive (and yet is killing her) ... thats it ... is there anywhere in forgotten realms lore said that nobody besides Barbarians can get angry?
(Hint: No, it isnt ... quite the oposite, in THIS VERY GAME you can angry multiple NPCs that are not Barbarians ... among others, mainly Ketheric Thorm.)
And last but not least.
> Gale was a Wizard ... i believe you know how past tense works, do the math yourself.

Those are their stories, that were "tightly coupled to their class and identity" ...
Abything beyond that, is just your own lack of imagination.
Incidentally, I don't recall past BG games allowing you to
Well ... since we are not playing, nor even talking about "past BG games" ... i dont see how is that relevant.
And even if we would, just bcs something "was certain way" it doesnt mean its "the only correct way and should never change" ... few examples from top of my head would be: Slavery, Witch-hunting, or Experimenting alive beings ...
Be glad humans can evolve beyond their past ... sometimes its a good thing.
