Remember, back in previous editions, we had "Good" clerics that used radient energy while "Evil" clerics used necrotic energy? That's what the Death Cleric is. The "evil" necrotic energy using cleric. The name is a misnomer, as this subclass generally has nothing to do with actual undead. Its the subclass for the stereotypical cleric of an evil god. Life is the stereotypical "good" cleric and Death (as the opposite of Life) is the stereotypical "evil" cleric.
Trying to say you can be a neutral Death Cleric is really just splitting hairs. The Death Cleric is the subclass for a cleric focusing on murder, disease, pain and destruction. There's some undead stuff in it, but that's generally the type of thing that neutral death gods like Kelemvor and the Raven Queen oppose. Now, a "god" that is happy with undeath, like Orcus (well, he's got clerics, so close enough) or Nerull, would be down with the subclass, but not the death gods favored by most adventurers. So, while technically you can be any Alignment, the themes and mechanics of the subclass really aren't neutral. I would sooner suggest a different domain if you wanted to do a Kelemvor/Raven Queen/Wee Jas cleric, as the Death Domain has little in common with those gods' doctrine outside a tiny nod to undeath. And a really unnecessary one - all clerics get access to the ability to raise undead from spells. You can just as easily play a psychopomp-themed cleric as any domain (Life, Arcane, whatever) on top of the undead theme with no problem at all.
Now, I have no problem with people playing evil characters (as long as its someone well thought out and not an excuse to be a disruptive jerk), but I would want the player to own up to what they're playing. I don't even care if they pick a LN alignment. But if you're playing a subclass that's filled with killing magic and necrotic energy, that should be acknowledged as part of the character.
Actually, why did WOTC tuck death domain in GM guide, because it's evil, but have warlocks making pacts with demons in player book?
Tradition would be my guess. Fiend Warlocks, Assassins, and Necromancers are traditionally PC material, despite the evil overtones, while evil-themed clerics are not.