I think that the cat should have more powers. Cats are very good at killing snakes and birds. This should be possible. The only thing you can kill with the cat is the mice.
Hi,
Sure, cats can defend themselves in real life, but this game isn't really about that kind of action.
This game heavily relies on a certain situational awareness, tactics and precise execution. The essence of the game (at least the action) is that you control (move/position) the cat and by doing that you can lead the girl into a position where she can protect you while you collect the artifacts (her memories). In a sense, she is your weapon and your shield.
By giving the cat the possibility to attack pushes the game more to an action category and the girl becomes pointless to be at your side. It would be a very different game.
Maybe in a possibly sequel there will be some changes in that direction.