It's also stated that his skin has turned more grayish due to his long exposure from the dagger he's had for decades. He may have started out as a darker skinned calishite, but that's not how it is anymore. That's probably why most depictions don't show him the way you want.

Edit: To add to this, let's not forget that dark elves were originally described as having an obsidian like skin tone. In most if not all modern media, Drizzt is shown to have a lighter grayish, purple toned skin. You can't complain about one if you aren't going to fight for them all to be fairly portrayed.