"Making the Darkin just want to kill everyone lacks depth/is boring" ... BUT

But that's exactly what they want to do. The mortals (humans) literally managed to kill off the majority of them, and the ones they couldn't kill were imprisoned. Knowing that they are entirely evil, it makes perfect sense to have them want to kill every mortal.

I will agree, this is a little bland. But it makes a ton of sense, and that honestly means more to me than to give them depth. Riot tries to manage depth within their story rather than their character. Well, except Aatrox, but he's due for an update anyways. Varus tries to have depth with the story behind a gay couple just trying to stay together for as long as possible but accidentally (not really) giving themselves over to the darkin Varus. Rhaast is the story of perhaps one of the most powerful (not politically, but literally) men in Runeterra being full of himself and going "Yeah, I could do that" before deciding to pick up the dark Rhaast in scythe form and beginning a battle of wills that ends in one being dying and the other gaining what they lost.

Aatrox wants to kill everyone because he lost a battle. Varus is just mad at the humans for killing 99% of the darkin. Rhaast just likes killing, and there's probably some underlying feelings of vengeance in there somewhere.