Also, for me, the personality-related line of argument lost all legitimacy the minute they said Damian could be Robin.
Okay, here I have to agree 100%. Damian does completely make a mockery of all of it, and no one deals with it like it's a problem at all. (One could argue that his basic level of survival skills is high enough that he avoids those dangers and I'd agree, but those aren't the only personality problems that have been considered an issue in the past.) So the treatment of Damian is completely hypocritical and immediately makes their treatment of Steph unfair, I agree. Total double standard, not just for Steph but for Jason, and for me it's another reason that Damian creates serious problems for the Bat-verse whether or not I like the character or not. I don't even think this is the only way. Damian is totally getting treated differently.
But forgetting him for a moment and pretending it's before he showed up, I think the judgments about Steph not being suited to the job were adnd still are perfectly reasonable. That it seems impossible to talk about her mistakes without a ton of criticisms of Bruce and everyone else for not treating her correctly doesn't make her seem more capable to me. There are times where I'm reading along and think the writer just demonstrated something that is a reasonable thing to get her rejected, and it gets described as Bruce's fault because he did something that would make her do the wrong thing.
It's Bruce's fault because he doesn't know how to work with her. But why would learning how to deal best with SB be a priority of Batman's? Steph's personal experience and development becomes central in ways its not with the other trainees. This seems to me exactly what makes other characters not want to work with her, because they feel like it's up to them to make sure she's not doing the wrong thing. They can't not feel responsible for her because they don't trust her judgment. And the more her actions are the responsibility of someone else the less reliable she seems to me. Not because others won't ever make mistakes, but because they'll be better at dealing with mistakes as well.
It's not just that she argues, it's when and why she argues, and what she seems to learn from arguments and experience. I think she's had things explained to her, or shown things that should explain things, and continues to argue or just not get the lesson. One can decide it's just Bruce's fault for being a bad teacher, or being a bad teacher for Steph (though it's not just Bruce), but that still adds up to her not progressing where other people have.
People have described how they find her appealing because she continues to do this in the face of everyone telling her she's not good enough. Which is a fine reason to like a character but not, imo, a reason why those people must be shown to be wrong for telling her that, or why her doing the same thing should eventually be rewarded with different results.