Not sure what the exact point is but the whole "champion X can't do this and there would be uproar if they did so can we not let Champion Y do it" logic is pretty one dimensional. It fails to take into account... well, anything and everything else.
In your example, Darius has more utility (even if it's "just" the pull), durability, and healing than Katarina. She has more movement potential and (I guess?) damage, at least more burst. You're comparing an assassin to one of the stronger juggernauts.
Also, under what conditions are you arguing that she is "one-shoting" someone at level 6? Not that I'm necessarily saying she can't, nor would I be too surprised if she could, as she as an assassin, and this is also a "everyone bursts everyone down" day and age of League, but I just want ask because exaggerations don't strengthen arguments, so I want to ask to make sure that's not the case.
Anyway, to my understanding, more AP is given (and isn't it 0.6 AD for every 1 AP, or has that changed?) because of the nature between AP and AD whereas the former relies more on cooldowns, compared to the latter which gets benefit from auto attacks (and many AD users also get more attack speed too atop this). If they gave an equal amount, it'd favor AD.