Just to be clear, I'm mainly arguing devil's advocate as to why people might feel the way they do about Lae'zel, I in general don't mind her as she is now despite what I see as flaws in her writing. Though there are some parts of your arguments that I disagree with still.
I'd say people get this idea from the fact that she 1) was found caught in a tiefling trap that she apparently needs us to free her from
1) She dont need us ... if we leave her there, she escapes on her own ... we are just usefull tool that makes things happen faster, nothing more.
2) This is awfully out of context ... yes, she was in the trap, but litteraly just few moments earlier our "strong character on wich she should rely" was lying unconscious with face burrowed in beach sand ... Shadowheart aswell.

I mean ... applying the same rules ... our character should be seen just as weak and dependent as her.
I mean, if we don't make right for the creche then we're not all that useful and we only slow things down for her. As for your second point, it's true, but we also were not stuck in a trap. And the fact we have to rescue her does create an impression that's unlikely to go aware unless you sit and really peel back everything about it,which most players, especially on a first playthrough when they're just going through the game, aren't likely to do for such a basically straight forward moment. If we just found her passed out on the sand, that would feel different. Instead we find her in a trap she needs to get her out of. Plus we're the main character, we naturally attribute to ourselves greater benefit of the doubt since we're seeing things unfold through our own eyes. It's why I mentioned it not being clear when she got into the trap. We were unconscious from falling out of the nautiloid. totally fair that she might be put into a cage while unconscious. But the impression given, as you seem to point out, is that she was awake and moving about when she was caught, which makes her seem less competent. It's not entirely fair or strictly logical, but by story logic, that's the implication.
2) she's travelling with us and listening to us as we travel.
Well, this is argument that is really hard to take seriously ...
We are main character, our followers were made to follow us ... duh ... :-/
No, it makes no sense ... but not many games do all the time.
Why Kazuhira give orders to Venom Snake, even tho Diamond Dogs as organisation "belongs to PC" and our ingame nickname is Big Boss?
Why Aleister get orders from our PC Grey Warden, even tho he have years of experience and we become one litteraly few hours earlier?
Why Emhyr var Emreis didnt get Geralt killed, when he mock him on his own court?

I could probably find more examples, but the point is still same ... bcs the game is telling OUR story, no matter how small or big cogwheel in the whole machinery we are, we still are at its center, everything is turning around our PC character.

So, sorry ... but you cant really use as an argument that NPC do what it was created for. :-/
I agree, but the problem here is that the answer, obvious as it is, requires the player setting aside the logic of the story and the character as presented to instead just say, "it's a game, don't worry about it." And while I'm fully in favor of saying that when it makes the game more interesting, I don't think it does so here. I'll point to your dragon age example in particular because that's the only game you mentioned I'm familiar with. Alistair actually gets asked why he's taking his cues from a new recruit when he's at least a year or two more experienced (the sense I've always gotten is that he's still 'the new guy' himself relatively, but he's been around long enough to know the ropes). And he gives a reason. He admits to not being comfortable with leadership and preferring to take orders from someone else, and our character is the more assertive force, the one who's willing to take charge. So they took that fact of game narrative design and made the story work with it by tying it into Alistair's character. It's even something that can impact his character arc if he becomes king or not.
So while I don't think the 'because it's our story' justification is bad in general, it's bad here because as written, Lae'zel's character runs entirely counter to her role in the story. Which is what I man when I say that it's a failing of her writing. If the only reason there is for why she doesn't leave us is because we're the main character, then that's poor writing. It means Larian failed to consider the limitations of the medium they're working in.
Based on her personality as shown, if she really thought she was capable of going on her own and not relying on us, then she would kill us all and leave.
I would welcome such outcome ...
But im affraid im in the minority here.
I think there's still honestly a bit of an issue here because she's SO rigid, so set on only one goal that it wouldn't make sense for her to tolerate any but the most absolutely necessary diversions. To the point that taking on basically any side quest should be unacceptable to her. And having a companion who requires you to ignore most of the fun parts of playing the game isn't that great an idea. It's basically setting her up to be fundamentally unlikeable not simply because of her attitude, but because she's stopping you from engaging with the game.
but i certainly loved when Sven attacked my character in DA:Origin, bcs he disagreed with my leadership ... and only after he was "put in line" he submited. :3
When I saw this said "Sven" instead of "Sten" I thought for a moment you were referencing a very strange moment in a Panel from Hell. XD
and so when a character is on the good guy's side and clearly starts off as evil, then if people like that character, they will want the character to become more good.
This is something i dont really understand ... even tho i see it very often around me, in real relationships.
Two persons meat each other, find something they like about the other ...
Then they both spend lots of time and energy trying to shape the other more in their own image ...
Usualy one submits sooner or later ... in better cases, they broke up, bcs they give up ...
But if not, somehow in the process something is lost, something that made the other character interesting ... or, if you wish, make them what they are, at least partialy.
Then its only matter of time til sucesfull shaper find out that he dont like this new person ... and they broke up anyway.
What's not to understand? People like to have control over things, and sometimes that desire for control extends to people. In a real life context that impulse is always unhealthy. In a fictional context, it's only sometimes unhealthy simply due to the way games work. And with games, people understand that being evil is not... well, good. In fiction evil is usually presented as ultimately futile. It's harmful, caustic, and most importantly, it doesn't provide an avenue for genuine happiness. And when you think of it in that way, why would anyone want a character they like to be evil? Especially because Lae'zel is on our side, not a villain. Villains are different because we're rooting against them. We're rooting for Lae'zel in as much as we're rooting for our side to come out on top. And that extends to wanting her to be happy. And thus, wanting her to not be evil.
Possibly ...
Problem with games is that such changes often happens so fast, its almost parodic.
Just look at her ...
She is certainly at least 20-30y old ... with no idea how much time she spended in Astral Plane, where they dont age ... so it can be even centuries ...
And during all this time Githyanki doctrine was the only thing she even knew ...
For lets say those 20 years ... she was told that she is supperior in every way ... even if you would beat her, her indoctrinated mind wouldnt see it as proof that it was a lie ... she will understand it as her own failure, bcs doctrine is right, it allways were, and it apply to everyone, so logicaly it have to be her fault.
Thats why i like it so much that she is mad at Kithrak and suspect him from betrayal, bcs that makes sense from her perspective.
Yes, we (players) know that Githyanki are backstabing assholes that only allows you reach so far, before their own queen will devour their soul so nobody too strong will ever appear ...
But Lae'zel have no such information, in her eyes Githyanki are perefectly oiled machinery, that works for centuries, maybe even millenia, under watchfull eyes of her beloved, strick, but fair ruler ...
If you take this all under concideration, how should our little adventure that (in EA) takes barely few days could outweight decades of ... well, basicaly brainwashing?

Even if our full adventure would take year, it would still not be sufficient in my eyes ... unless something so drastic (and dramatic) would happen, so it would right in front of Lae'zel eyes give her undeniable proof that her doctrine was wrong!
And such thing would have to be Vlaakith trying to kill her personaly, in order to get the Weapon.
Only after this i would concider her questioning her values.

But that is probably just my opinion.

I don't think you're wrong anywhere here except for two points. The firstand least important is that I believe she says explicitly that she's never actually been to the astral plane, she's been living in Creche Ki'lir, on the asteroids that follow the moon in the material plane. The second, slightly more important point is that I don't think it would necessarily take only Vlaakith herself trying to kill her to make her change. I think if the writers wanted to, they could write plenty of emotionally wheighty, intense moments that could convincingly see her change. Not all at once, probably but still.