There are enforcers for a secret society who consider themselves entitled to behead children for breaking rules they don't know exist, and they do it right here in Chicago...and you can't interfere. You have to look the other way.
There are whole families of super-powered sex predators and rapists (the White Court) who prey on innocents, sometimes to the point of death, rape their minds and bodies, right here in Chicago, including teens (at least)...and you must not try to interfere.
And so on. Do you think the Karrin of that time could have accepted the necessity of looking the other way? But if she doesn't, a lot of good cops die for no reason, other people's lives get shattered, probably some cops end up imprisoned (which can be a fate worse than death) by the supernaturals manipulating the system, her family might pay a steep price too? Could she accept the reality of that, before the loup garou rubbed her nose in reality?
Actually Harry if you will remember didn't feel that Karrin should look the other way.. He was horrified about the kangaroo courts that the Council held or often didn't bother with before they chopped off the heads of kids they felt were going warlock. No, Murphy wouldn't accept the reality of that, but the truth is, neither did Harry.
He accepted it enough that he knew he couldn't stop it. He accepted it enough that he knew he had to keep Karrin in the dark until she was ready to face up toe the cold fact of the Council's overwhelming power.
Yeah, he hated it. He
still hates it, he just knows it's necessary now. He's still casting around for some other solution, but so far he hasn't found one.
Actually you can argue that Murphy did accept it, she had no problem acting as judge, jury, and executioner for Nic in Skin Game, though she claimed she was no longer a Holy Knight she used a Holy Sword in an illegal manner. While doing that she also violated every oath she ever took as a police officer and got a Holy Sword shattered.
Yeah, but that came much, much later. The turning point for Karrin was the
loup garou rampage at the police station. That forced her, by brutal example, to accept the reality of the overwhelming power of the supernatural, and that she cannot be in control when dealing with it. It rubbed her nose in reality.
Even after that, she would periodically start to slip back into her former mode of thinking, because the Law was her comfort belief, and because she desperately hates feeling out of control. In
Death Masks, when they were about to go up against Mavra and her minions, she has a moment when she suggests to Harry that they could do it the legal way, bring in a mass police force to deal with the problem.
Even Harry is tempted by it. But he knows better, and deflates Karrin's bubble as gently as he can without indulging her fantasy. This sort of thing happened several times over some of the middle books, and usually Harry would have to remind her of the
loup garou to bring her back to Earth.
In
Proven Guilty, when Harry tells Karrin about the execution of the Korean kid, her first reaction is fury and probably an impulse to call for arrest warrants. After all, the incident was, by definition, First Degree Homicide with a minor as the victim, and a number of other felonies as well.
But Harry (who was similarly angry about the whole situation himself earlier) has to remind her that the police couldn't have handled the kid, there was no mundane jail cell that would safely hold him, and he reminds her reluctantly of the
loup garou again, IIRC. Then he rather reluctantly admits, to her and himself, that that White Council really has tried, repeatedly, over the centuries to find a way to rehabilitate warlocks. Nothing they've tried ever works once the warlock slides past the edge.
Murphy reluctantly acknowledges this, and to salve her pride says she can't ignore a dead body if it's found, and Harry promises her that it won't be. But of course even that is just her pride talking, if the Council ordered her to hush up an investigation, body or not, she'd have to do it. They're just too powerful to disobey.
She also starts to slip into it in
White Night, but then she has an encounter with a Gruff that reminds her of the
loup garou without Harry having too. She bluffs her way through the encounter at Mac's, in a way the ends with Mac and Harry deeply impressed. But truthfully, they really shouldn't have been. She was bluffing a representative of a supernatural megapower, and if the gruff had called her bluff...well, that would have been unpleasant. She shouldn't even have tried it. It was a Cool scene. But an unwise moment.
I suppose that's an example of my older self's perspective, actually. Bluffing is what you do when you have absolutely no other option. Bluffing to salve your pride is foolish, and can get you into a world of hurt if you're not lucky. My younger self saw Cool, my older self knows the wisdom of the old saying, "When in doubt, STFU."
That same pride eventually did lead to her shattering a Sword, as you note.