I think the main issue that has to be dealt with is Murphy's sense of purpose. Not only has she lost her position with SI/Chicago PD, which was what had defined her internally as well as externally, she has now caused the unmaking of one of the swords through her own actions. In the privacy of her thoughts, that has to be devastating. A few times now, the supernatural villains of the story have referred to Karrin as the "fallen cop" or the Broken one. Whether that is meant to be just a taunt or whether they see the truth of Karrin on a deeper level, I don't know. Being kicked out of SI was not her fault; she had done nothing wrong in any sense. The sword unmaking was entirely on her. First in appointing herself guardian even after Harry returned, and then of course her actions in Skin Game that caused the Sword's destruction.
As much as I could see her dying and becoming an Einharjar, I agree with those who argue that there has to be a character that tethers the story arc to the mortal world. Murphy has done that up until now. But she needs to regain a sense of purpose within the mortal world. Personally, I would love to see her go FBI, and team up with Tully. That would give her law enforcement purpose again, but on a larger scale than SI. It could also put her in a position where responsibilities would often take her away from Chicago, meaning a relationship with Harry would become harder as well.
The Murphy the Broken persona is getting real old. If nothing changes in Peace Talks, I can easily see Jim bumping her off as just one more point of pain for Harry. But if he does, the story will have completely lost its mortal moorings, which would be a real shame.