Firstly, I think they try too hard to "differentiate" the Batfamily members sometimes. They end up pigeon-holing them as just one thing. I've complained before, especially, about someone deciding that each Robin is basically one concentrated aspect of Bruce instead of each having a fully developed skillset in various areas. Tim is the Detective - so no one else is. Which is ridiculous. Dick's detective skills were highly praised for years, and then later he was kind of a flake, which is so sad. Tim was used to be well-rounded, despite having some issues, and became broody and miserable (understandable, since Steph, Jack, Dana, Kon, and Bart were all killed). And went from a smart kid to super genius.
Here is a post I had with some irritation on that. Sometimes it feels like they can each only have one dominant emotion/personality-trait - instead of each being a whole person, they each have to be an aspect of a whole person. This probably happens more when they are together, but wouldn't swear to it.
Also, I think later on sometimes (not at all always) something of Steph's demeanor gives the impression of being a bit ditzy/flaky. Not the
reality of her actions, you understand, but the demeanor, the language. This happens to Dick some, as well, later. And I seem to recall it applying to cartoon Starfire, but it's been a long time since I watched that Teen Titans.
What made me interested in Steph in the first place was that Batman didn't want her working in Gotham, but she did it anyway. She did not submit to his authority. The pregnancy storyline sounded interesting (it was okay, but sometimes went a little after-school-special). But mostly, it was that she worked independently, though in Bruce's city, and under no one else's authority. I liked the idea. So that's why I picked decided to read. As I read, I became more frustrated with Batman, and how he orders his family around (and
they do what he says) and how he acts like he's the king of Gotham and gets to decide what happens there. I liked her because she was likable - it pretty simple. She was struggling for acceptance,
had a mother she loved but couldn't rely on, was trying to find her place, and having some fun and trying to improve. And Tim and Bruce were not supportive, but she didn't let that stop her. Despite being rough around the edges and inexperienced, she was generally capable, if reckless. She's a bit insecure, and it's understandable that she is - in a professional sense because they keep telling her she is unworthy, and in personal sense because not only does Robin not tell her his identity, but he doesn't exactly invite her to hang out with Young Justice and him, either. He's in every piece of her life, but kept her walled off from his, and she doesn't know how important she is to him. After she finds out his identity, things change a bit.
But since I really like the independence aspect, you can see why I'm not exactly a fan of her being Batgirl (or Robin, even if had been done to deliberately make her a failure and kill her off). She's become subordinate to someone instead of being her own boss. Heck, Barbara is even her teacher, too, so has some authority over her in that aspect of her life as well. I know that being accepted into the Batfamily was meant to be a promotion. But for me, it's a demotion, because she went from being independent to at least sort of answering to someone else. Worse, they treated her so poorly. It's Rudolph the Red-Nosed Reindeer - you're supposed to be happy that all the reindeer love him now, but I want to tell them to go screw themselves. Obviously, the most mature, most self-confident reaction is just not to care anymore what those people think (see Jake Stone on the Librarians for an excellent example), but it's not necessarily as fun, and it's not really a place you think Steph would be at that time - emotionally recovered enough for that. Heck, I might even feel better if they said she'd earned Batgirl, but then it seemed like she was given out of charity, because she needed it. That I did not like, at all. It's one thing for Damian, and an entirely different one for Steph to me. And then, you know, sometimes it's like having the title makes her worthy of respect/regard instead of herself making her worthy of respect. And they (at least Barbara) can take it away anytime they want - just like Bruce did Robin. At least that's how it is in the early issues of Batgirl - it may change later, but I disliked the vibe enough I haven't read many issues (I did read a couple later ones).
But mostly, it's because I read and liked the character, and then she had a completely different characterization. Personality-wise, she's like the same in name-only, almost. This happens all the time in comics. And so I have a lot of characters that I only like in certain eras or at least that I strongly prefer the characterization of a certain era and don't really care to read others (I gave list in a previous post).
Here is a post about someone who finds New 52 and post-COIE Barbara to be like two different characters. A very understandable perception, IMO. I can sometimes feel similarly about late '90s and late '00s Tim and Steph. At least Tim has stuff that would make him act the new way (so much death) - I don't feel like anything that happened in Steph's life would motivate her to start throwing wisecracks and being extremely cheerful.
I don't like dark paths and I certainly don't want anyone to be him. I don't even want Bruce to be post-COIE Batman. Got annoyed when Tim and Dick and even Barbara pulled some of his tricks.
Thing is, she gets treated like this (by fans) in the present tense (and even before N52). She might have been canonically far less capable when she was Spoiler, but she was a far more serious character (in a day-to-day-interaction sense, not claiming she didn't have any angst later).