You have to remember how she was in the first three books. She was a thorn in Harry's side, being an obstacle for him to work around, or a distraction.
I think it was just the first two books. I can see an argument for a distraction in GP, but I disagree.
Murphy has served a functional role in every story she appears in. I just don't think there's a whole lot that she's done that Butters, Stallings, or Rawlins couldn't just as easily have done on the CPD side of things, or Michael and Thomas could have done on the muscle side of things. And now we have more options for that, so it's easy to imagine Jim could have introduced another character to fill these roles. Bradley is
better at being muscle than Murphy. Murphy never beat him in a match. He'd also be a good character to have around for people starting the books at this point. Same goes for Tilly.
I just don't see how Murphy has been a foil for Murphy. I really think she was more like Harry than different from him. Butters (before he became a Jedi), Michael, Marcone, Nicodemus, and maybe even Carlos are all better foils for different aspects of Harry's character than Murphy was. I'm not big on literary analysis, so I could be missing something. I prefer a more Watsonian approach.
And she was black balled from any law enforcement agency, which was who she was to the core of her being.
People change, especially when they have to.
As for finding a place, she was losing pace to the rest of the group. She wasn't getting a power up. ... So no job, losing step to the supernatural group, no powerup to work with, there really wasn't a place for her anymore that was in the main part of the story. She was just slowing Harry down.
Murphy's physical prowess was never what made her a threat to the supernatural. They all had her beat physically. It was her willingness to admit the supernatural existed and then deal with it intelligently. Jim could have easily moved her into a command and control position instead of a combat position. She would have been perfect for helping Harry run whatever group he's planning on going with if she could have adjusted to not being on the front lines. She had done that in plenty of books. Sure, she was moving away from it by BR, but she was still filling a largely non-combat role as late as TC. She was also being more of a leader than we've ever seen her be in GS. The groundwork was all there for a difficult, and maybe failed, transition from a front line soldier to a leader.
I know I said I didn't care what Jim did with her the last time we had this debate, but I'm starting to think her trying to make the transition, failing, and then dying as she takes the field would have made a better end to her character arc than her never really trying in the first place.
I'm still undecided on whether her trying and succeeding would have been a better or worse story choice than what we got. It probably would depend entirely on the execution.