Since Riot seems to not consider Karthus's kit toxic enough for a rework (Taking a backseat to Morgana whose kit didn't even change with the update), perhaps a change to his kit would make him less keyboard smashy.
Karthus should be punished for positioning like an ape. If he dies the first three seconds of a fight he shouldn't still be able to spam Q a hundred times and then ult. And while we're at it, make it non-global.
You could double the damage that it does and drop its CD significantly if you do these things. Make him have to damage his ult targets with a non-ultimate ability and be alive in order to ult someone. Add it some skill requirement and increase it's reward for executing it correctly.
As it stands Karthus is actually rewarded for dying immediately since he is immune to crowd control while under the effects of his passive. People complained about "inting scion" and "inting kog maw", but Karthas is the only champion who could int the start of a fight and then headbutt his ult for a pentakill.