The problem with Katarina
The problem with Katarina isn't her scalings or her QWER or anything like that.
It's her passive. Everytime she gets a kill she gets ANOTHER QWE.
Which would be fine on almost any other class of champion but it is a really stupid passive on an assassin. An assassin is supposed to choose their target wisely, swoop in, kill that target, and then escape or die.
However Kat's passive makes her a very Hit or Miss champion. If she is able to kill ONE person, she is able to kill another...and another...and another and another and before you know it the whole team is dead.
On the other side if she fails at killing that first person...she is dead.
Like isn't Riot trying to fix champions that either Penta or busts?