Katarina isn't the problem
I see thread after thread about Katerina damage/op and feel it in plenty of games surely but what everyone seems to ignore is that the only thing that threw her over the top is her synergy with ludens Echo.
It adds aoe to her aoe speeding her clear Nearly doubles the damage of her dagger Gives ms Procs constantly thanks to her teleport And has no penalty associated with mana as it would other champs, and no penalty for not getting random (because her ratios were never really amazing outside of a vacuum.
Once we add its proccing enormously if resets come in the damage far surpasses anything the dfg used to add because it affects multiple targets multiple times in short succession.
That same tiny additional damage means she almost never has to rely on aa's to finish minion waves, nor does she need to dive in to get the mark damage proc because the damage of dagger alone is no longer neglible.
-- really I don't see a good solution to this particular synergy but it was bound to bring certain champs over the edge exactly as it has. Another angle needs to be found than nerf Kats ratios again, they aren't the prob.