IMO it has nothing to do with Odin. The Swords (or at least their true purpose) were never Murphy's style.
She's great when fighting outright monsters like the Red Court, but... well, she was always about punishing the guilty as much as protecting the innocent. It's like she said to Harry in Skin Game:
"I don't want to save [Denarians]".
That is the core of the issue. And to her credit, she knows it- it's why she rejected the thing in the first place.
Which is at the core of why she managed to break the Sword of Faith. Key word here is
faith,she had all the faith in the world in her own judgement, but none apparently in the ultimate Judge. She spoke out of both sides of her mouth when she said she couldn't return the Swords to the appointed custodian of them, Harry, because she feared that he'd screw up giving them out somehow and get them broken.. Why? Because deep down she didn't trust Harry after what had happened to him. Meanwhile she kept the Swords because she believed she had better judgement than Harry.. Then after her little speech about why she couldn't be a Holy Knight, for fear of what it would do to the Sword. She proceeded to desecrate the Sword of Faith by proclaiming it was for her to judge Nic,not the Lord,then tried to kill him with it, and got it broken. In a word, she's a bit of a hypocrite.. Maybe love does that or can do that to a person, but in my opinion Jim killed her off as a character long before she was actually killed off, beginning with Ghost Story when he made her a vigilante, he systematically stripped her of all the virtues and strength that made her a great character in my opinion.. Her abilities as a fighter, her great love story with Harry don't make up for all that she lost.
And I for one do not wish her back.