IMO, a close and personal melee class makes most sense as the Dark Urge: - Rogue, Fighter, Barb, Monk.
But there is only one true fit - and it is a Rogue, especially Assassin, because
in Gortash Journal it is described how he and Dark Urge robbed house of wonders, and also stole the crown of karsus from the hells. Also, a Dark Urge specific cloak gives you invisibility on kill - perfect for sneak attack. With this cloak my Rogue playthrough was ezmode from start to finish. If you wanna go full BHAAL mode - of course it's an Assassin. Bhaals Chosen are Assassins, simple as that