Okay, this is stupid. A trebuchet is really bad at aiming mobile units. Sure you can load the shuriken barrel, but there is a problem: the barrel rotate, so when it explode, the shuriken will fly everywhere. That's why it worked with the ballista: the barrel stayed in the same direction.
In fact, a catapult would be more efficient than a trebuchet to hit flying enemies because a trebuchet is slower, hence more chance to fire and hit with a catapult.
As for aiming: with a trebuchet, you fire your first shot, see where it lands, adjust in function of it. So yes, it can very precise, but it take multiple times.
Let's not forget that trebuchet need to be stationary, or else the aiming is off. Not ideal to respond to fast flying attack.
Trebuchets are mainly a siege weapon. Even as a defense weaponry, it wasn't the best, it could be used to destroy siege tower or distant siege weapon, slightly disrupt the formations, but that's all, the uses were limited. It was more like a counter to siege weapons.
The trebuchet is king of the siege weapon, but let's not give it the crown for everything