Alice knows Kate's secret identity. She doesn't need to defeat the bat-suit, if her objective is to kill Batwoman. Plus, the bat-suit hasn't protected Kate from her own mistakes, even from villains without the secret knowledge. So, it's not meshing well now. Maybe later it will get good again.
Another thing to remember - the book was written while Bruce Wayne was bearing the batsuit so it would have been about bringing him down.
That Kate wears the same suit and uses the same techniques means it will also work for her.
or it the "killing" doesn't just mean the person in the suit but what they stand for.