It's perhaps noteworthy that the one time she does "beat" Freydis, her victory is based on her willingness to die to win.
If she dies in Battleground, it seems likely that she'll go out in suicide-bomber style -- not a good end in Catholicism, but perhaps honored by Valhalla.
It was a surprise and over in seconds, not clear how hard Freydis was fighting back or at all. She might have been merely testing, also it really wasn't the time to have a knock down drag out, her
current boss Lara needed Harry or at the very least wanted to talk to Harry at that moment.
I know everyone thinks it, but I doubt that Murphy will become a Valkyrie for a number of reasons. First one she doesn't respect authority, not a good idea to argue with Vadderung... Yes, she has worked with him in the past, but as a mortal she was also free to walk away.. As a Valkyrie, not so much, not sure she'd like the idea of knowing in advance who was going to live and who was going to die, especially if she didn't agree with it. Yeah, I know Gard fudged with Harry back in Dead Beat, and perhaps Michael in Small Favor.. Yes, it does go against her religion.. Nor does it mean she can remain at Harry's side. So she may become it in the end, but it may not work out as everyone thinks it is going to be.
Murphy like Dresden serves the greater good, Harry doesn’t shy from taking on the Titan even if it will kill him, he is acutely aware of this and won’t stop even for Maggie (but he will make arrangements in the event of his death) for goodness sake being nearly dead didn’t stop Harry in Ghost Story, so being crippled won’t stop Murphy, she will do what she can, which will likely be leading SI and CYPD into battle. Her fate has always been to come back with her shield, or on it. She will never surrender.
Harry in Ghost Story isn't the same, or even close. He was trying to find his own killer for starters. Second of all an archangel arranged for his walk about.. Also if you will remember there was very little he could do to help those who were very much alive.