The advantages of using a catapult and battling ram during battle were:

The answer is: You could toss plague victims onto enemies castles and destroy castle walls

At that time, the knowledge in medical field still hasn't developed yet. So, there were no empire that able to find a way to cure plague infection.

Because of this, enemies that have resistance to the plague often use catapult to throw plague victims into enemies castle and spread the disease ti kill a lot of soldiers effectively. They use the battling ram to smash into castle's door and create a small hole for their soldiers to pass through.