Your big beef is that I don't have enough experience or training, and it's dangerous, right? Well, I've A: been doing this for almost as long as you have at this point, B: at this point, I've actually been trained by more people than you have, and C: Bats himself - your boss - your currently dead but oh so all-important, all-critical jerkwad of a boss - has given me the thumbs up by now, and asked ME to help HIM with YOU! Stop whining about how I can't do the job!'
Actually, I think the beef at this point isn't that she doesn't have experience or training but that experience and training aren't enough. I don't think Batman ever did fully give her a thumbs up, but he does use her when he thinks she can be useful. Most recently telling her to sort of throw things at Tim knowing that if Steph was the one creating the scenario it would be Tim who had to fix it--iow, it wouldn't be a training exercise, it would be the real thing. At least that's the way I read the position of the others about Spoiler.