Karthus's design is stupid and is the most poor-play-forgiving champion in League of Legends.
His passive lets him do a majority of his damage even when he gets caught and dies immediately. When he is dead, you cannot silence him, you cannot stun him, you cannot push him away, you cannot do anything other than get out of his defile and survive his ult. His kit makes it so that no matter how bad he did, he can always farm back up and pick up a few kills from finishing off people in teamfights and then proceed to carry because of his huge AOE potential and non-negligible ult damage.
Every champion has counters, but what is Karthus' counter. You have to focus him down or his AOE damage will melt you, but once you kill him, you still have to re-position and get out of his defile, and even then, he can still ult you. What the heck? Annie gets caught and dies before using any skills, GGWP. Cassiopeia gets caught and dies before using any skills, GGWP. Kennen gets caught and dies before using any skills, GGWP. But Karthus? Nope. He is the only champ who can still do a majority of his damage even when he gets caught.
And don't say build MR. MR will help against every AP champ, the fact that Karth will hit EVERYONE (Everyone needs MR) even when he's DEAD (Can't focus him down so he can't do any damage) doesn't make him any easier to counter with MR. In fact, he is probably least affected by MR.