Yes. Their jobs determine their class, unlike the others, who could be any class in order to be heroes. That's why I don't think they count in the same way, though the way they're written as moral and allies of Batman is still interesting; after all, there could have been stories in which they weren't, they might've become bad guys*, but they didn't.
*I think even with comics' love for status-quo that could've happened?
but I got the impression he was pretty standard in his abilities as Robin, with the main problems being emotional, which also sometimes led to him not being diligent. So his problem wasn't incompetence.
I had the feeling that the two were often linked. Given Bruce's emphasis on emotional control, it makes sense. Bruce tolerates Dick not being closed-off because 1)Dick proved that he's good enough to be still alive in spite of it (post-Jason, I get the feeling that lack of control = BAD FATED TO DIE for Bruce), and 2)Bruce likes it.
Jason's recklessness has been greatly exaggerated since his death. It wasn't being reckless that killed him, it was trusting his mother with Bruce's blessings. Steph, personality-wise, is close both to Dick and to Jason. War Drums - Gabrych in general - shows well the parallels between Jason and Steph. A lot of them are in Bruce's head, but it's an interesting comparison if only to think about what Bruce fears and what Batman looks for in a Robin.
There's so little making sense about the time Steph spent as Robin - even less making sense in Robin than in other series - that Steph being short-sighted is in many ways a retcon. I can't even blame Batman for not telling her he was Matches Malone, not when I'm supposed to believe that Steph would've seen the Case in the cave, would've seen Jason's name, and wouldn't have tried to find out who the kid was.
which she could have done as a girl from his own class, but she wasn't written as that.
Making her the Cluemaster's daughter was a handy and interesting way to put her in the story. Maybe DC thought Tim was enough as ar as upper class was concerned, and making Steph a girl from the same class would've felt too forced for the reader? I don't know, when I start thinking about how she could've been from the upper class, I end with the feeling that she wouldn't be Steph. She might be Kate Bishop, though.