Kai'Sa is just a worse Vayne
Kai'Sa's Q, since it doesn't prioritize champions, isn't a good tool for harassing in lane. Vayne's Q is, especially combined with her W. Kai'Sa's risk factor doesn't have enough mitigation either. While Vayne can spam invisibility during her ult, Kai'Sa only gets 0.5 seconds of invis while basically front-lining. On top of that, Vayne's W proc's true damage and only takes 3 autos to do so. Kai'Sa's passive takes 5 autos to proc and deals magic damage, which can be reduced. Kai'sa's ult is also useless in anything other than a duel, while Vayne's ult can be used to duel or to teamfight. There is no reason to pick Kai'sa over Vayne in any situation, and I think that Kai'Sa will need some changes before she can become viable as the "High Risk High Reward" champion she was intended to be. A few changes I could suggest are:
-Make her Q prioritize champions -Increase her AA range -Increase her E invisibility duration -Make her Living Weapon passive upgrades easier to obtain
Of course not all of these at once, but applying some of these changes could really help Kai'sa become her own champion instead of just being a discount Vayne.