I wish Katarina was an AD champ

Here's the deal. Katarina throws knives for Q and R, slashes with knives for W, and jumps onto someone with E. Why is she an AP champ?

Even though this is a huge change, as I mentioned above, hitting people with knives shouldn't be magic damage, in my opinion. Thematically, it makes more sense for her to do physical. How can we make this work in the game? My idea was to do something a little bit different with her damage scalings. What if she just did physical damage, but it scaled with AP? It's weird, I know, but there isn't any particular reason this couldn't work. Yes, the scaling numbers would absolutely have to be tweaked substantially, but I think it would leave us with a very cool champ, that still feels somewhat like her old self (able to build Z's Hourglass, deathcap, etc.). It terms of theme, this also makes sense to me. As Katarina becomes better at wielding whatever knife-guiding magic she's using, she's able to inflict more damage with those knives. Still physical damage.

In a recent patch preview, Riot mentioned that they've become very open to champs doing some really bonkers stuff (Azir summoning a turret, anyone?). This is an idea I've been considered posting since then, since this would make one of the older champs in league feel fresh and unique, but without actually changing her play pattern at all. Aside from thinking about whether this would work with Kat, what do you think about this "backward scaling" idea, in general? Even if you hate it with Kat, do you think it could work on a new champ, or a different old champ? Perhaps a champ that builds AD, but does mostly magic damage? Discuss.