Danzo knew that Tobi getting Shisui's eyes would be trouble and so he destroyed it before he died.

Itachi knew that Shisui's eyes would be trouble if they got into the wrong hands and so he burned them.

Nagato should have destroyed his eyes or told Naruto to destroy them. If Nagato's eyes had been destroyed the whole moons eyes plan would be screwed/stopped for the time being.