There are two problems with Katarina that work together to make her very frustrating to play against:
- She can unload all of her basic abilities almost instantly, allowing her to delete someone before they have a chance to react if she's fed enough.
- She gets to reset all of her basic abilities on kill or assist, allowing her to instantly unload them all again.
Personally, as fun as it is it to repeatedly jump to targets and get a pentakill, I think her reset mechanic needs to only refresh Shunpo and reduce the cooldown of her ult, while not affecting her other abilities. They have a short enough cooldown anyway, and having to back out of the fight and wait for cooldowns after getting a kill/assist would make her much more bearable to play against.
Though, that would probably mean she'd need a compensating buff in other parts of her kit.