Because she is supposed to be this thinking wise person..
Is she? I never thought that about her, maybe knowledgeable or experienced in some stuff that Harry isn't and that's why he gets impressed, but I never saw her as wise, or she wouldn't have fucked up many times.
She is also not thinking of the other people she could put in harm's way because of her injuries nor is she thinking of the people she is charged to protect.
In this point I do agree with you. She could have been a liability in the field, it wasn't safe for her to go, or for the people around her. It's easy to see how, for example, Harry could have get more hurt trying to protect her.
But she obviously wasn't thinking straight. And I think at that point was fueled by Mab's banner or whatever was called, the thing that energized people to fight or run, so Murphy felt she would be able to manage herself. Like Dresden does with the Mantle, not feeling the pain and all that. And she mostly managed. But maybe she would have died the moment Mab's energy was gone, since she was just unable to feel the pain, but could obviously get hurt, and all the battle would exert too much stress on her already weaken state.
and if she saw Harry as a commander in the battle then she should have done her duty
I don't think she ever saw him as a commander, so she had no duty to him. At this point in the story she listens to him if it seems like he knows more, but obviously doesn't see him as someone to obey. I think her speech in Cold Days is pretty telling, she tells him basically "wherever you go, I'll go". Not that that's right or healthy, but it's obviously where she is regarding Harry. Seems like it's all an emotional thing for her at that point.