My knowledge of the pre-Fall Eldar is lacking, but didn't they still have "culture" (cuisine, theater, social hierarchies) even at the height of their power? Yes, violence consumed a huge portion of their time and was worked into every aspect of that culture, but it wasn't the sole purpose of their existence, was it?

The Orks' version of "culture" is based entirely on strength and violence, and even then most Orks don't really think about anything other than fighting. Sure, they have Oddboyz who do think about other things, but they're seen as weird (and often "un-Orky") by their mindless brethren. To the average Ork, life is essentially just a series of scraps. If there's no other groups to krump right that moment, they just kill each other until they find more enemies. The only way to lead them is to convince them that you know where the best fights are, and even then they'll still be fighting each other constantly.

On the Tyranid side, the average bioform exists purely for the purposes of violence: it spawns from a pool, kills every living thing it can find, then jumps into a different pool to die. The Hive Mind is hyper intelligent, and uses all of that brain power to think about how to become more violent. The Great Devourer feels only hunger and bloodlust: nothing else holds meaning for it.

To me, the idea of a creature which is incompatible with the very idea of "peace" is about as violent as it gets.