Katarina is a very old champion from when design philosophies about how AP and AD worked were very different. They actually considered during the assassin update whether to convert Katarina into an AD scaling champion instead of an AP one in order to make her thematically more coherent, but in terms of pure gameplay patterns they felt like her itemization options in AP were better to keep as is (in retrospect, Edge of Night may or may not have been a huge part of this).
The new era of champion design tends to be more tight and logical when it comes to marrying design and gameplay, so I'd fully expect a character with sharp stabby knife legs to scale off of AD. That weird shieldy needle dive thing she does (perhaps an ultimate?) is the one demonstrated ability where I could see a case for some different scaling, perhaps an AP ratio (for Baron), possibly health ratio.