That's what the paladin Galahaad of Cenarion Circle is wondering. They look like zombies, they act like zombies, and they probably smell like zombies, so why are they classified as humanoids instead of undead?
CM Nethaera quickly responds that undead player characters were considered undead in the beta, but that was quickly changed after they found it created major gameplay issues. Undead are immune to fear, polymorph, and sap, but can be easily handled by paladins (Turn Undead) and priests (Shackle.) The Undercity would be full of paladins and priests, but elsewhere Undead would be destroying every Alliance player, free from crowd control.
If that doesn't satisfy you, Ninkasi comes up with a loreworthy explanation. The undead immunity to crowd control -- and their weakness to the Light -- are gifts of the Lich King. When the Forsaken broke free of the Lich King, they lost his gifts and his weaknesses. Some arguing about whether Forsaken are really evil in the eyes of the Light ensues, making me glad I'm not a paladin -- their forum talk about "an unnatural affront to the Light" reminds me strongly of televangelists.
Would Undead be willing to go back to being Undead if the choice were offered? A quick poll of my guild's undead on at midnight revealed one yes, one no, and one tossup. Priests, paladins, Forsaken: Would you rather the Undead be Undead, or are you happy with things the way they are?
Pictures are from the Madison Zombie Lurch 2005. Motto: "What do we want? BRAINS! When do we want it? BRAINS!"