Why does shadow Kayn ult have a high cooldown when compared to Yasuo or Diana?

Just an observation. Yasuo has a very low cooldown on his ult because he requires a knockup. Diana is similar because she can't do max damage with her ult unless she lands her Q. The same for Kayn. He needs to hit the target before he can ult. But, he has the same cooldown as Zed.

Now, I think the reason for this is because you can't have Rhaast gaining that massive heal from ult on a low cooldown. But because of this, shadow Kayn is penalized with a large cooldown.

So is the ult cooldown on shadow Kayn justified? Let me know your thoughts...