The Bloodthirsty divine ability is literally an ability that helps killers mutate in exchange for power. Just like mutation, it causes loss of control and grants power when used.
Not even legendary godclad and the god of killing can prevent the mutation and the loss of control that the Bloodthirsty divine ability inflicts on them.
The Bloodthirsty divine ability lets the mutation occur in a slow and controlled manner at the start. But once killers lose themselves to the power of the divine ability, they will never become sane again.
All in all, the divine ability is a double-edged sword. It is one of the reasons why the god of killing was considered the strongest god. But it is also one of the main reasons, if not the main one, why the god of killing lost his mind.