To me her story is about her coming to terms with the unfair death she has to face, and the struggles in doing so.
If that's the case and the writers really put effort into writing we trying every option, her struggles, and discussions following it, then fine, except it's clearly not. Like many others have pointed out, we didn't even get the option to try "trying every option", that's not tragic unfair death, that's called killed by doing nothing. The theme of a story means poo poo, how well the theme is executed is everything. The real problem of Karlach is not she is not saved in the end, but her story is rushed, poorly executed and severely lacks content.
Plus, that's just not the writers' original intention, otherwise there won't be cut content about her being saved in the game file, and her burning to ash scene in the end won't be triggered by a "quest failed" tag. Saying it's always writers' intention it's just like Larian saying upper city wasn't cut and Act 3 is always meant to be like that. BG3 is a game that tries to applease as many people as it can, it doesn't afraid to give anyone a happy ending, no matter how deus ex machina, inconsistent, corny or even cringe that ending is, and when it comes to Karlach it's just this? Come on. She's not killed by an unfair world, she's killed by someone's mediocrity and studio not giving a shit.