It does make a lot of narrative sense for Kate to die! It would be a point at which Max really has to face the fact that her powers don't give her complete control over what happens, and there are some things she just can't prevent. I can understand why you're able to save Kate from a 'it's good if the player feels their choices matter' perspective, but I think you make a good point; thematically, it probably works better if you can't save her.