Let's recap how this actually goes down in game play above 1200:
Karth runs in. Everyone focuses him. He Zhoyna's.
Everyone runs out of his AOE.
Fight continues, Karth pushes in again like an idiot even though he's almost dead.
Kayle times her ult perfectly and keeps him alive longer. People focus Kayle and she dies.
After Kayle is dead her 3 second (assuming max level, which I think is that long) ult is gone and Karth dies.
Everyone walks out of the AOE.
Karth ults.
Nocturne spell shields
Vlad pools
Support heals the ADC
and the AP mid uses their own Zhonya.
Really there should only ever be 2 people inside Karth's AOE: The top and the jungle. Maybe the Mid depending on the champ but otherwise the ADC and support should always be far enough away from Karth to not get touched by his Defile.