Can you say "Shadow Priest"? Sure, they don't have as many DoTs (three as compared to Warlocks' five or so), and they don't have any drains, but Mind Flay and Mind Sear do at least have similar animations. Not to mention, as someone else already said, Shadow Priests are able to remove their DoTs with Mind Spike.

I'm not sure what you're responding to Tyler. I don't see anything here that says any of the warlock trees are copies of anything, only that they are similar, which they are. Not to be deliberately obtuse, but I'm not really understanding how the fact that Affliction was designed, from the start as a "viable spec from the beginning" and Shadow was "originally designed to be a leveling spec", is relevant to the comments above stating that these things are similar.

Also, since you infer that it's an issue, what's wrong with Shadow Priests being a viable, Affliction like, end game spec? A thing was once thus, so always it shall be?

Our class as a whole has 6 DoTs: Bane of Doom, Bane of Agony, Immolate, Unstable Affliction, Corruption and Shadowflame. However, each spec can only keep 4 of them active at a given time since Immolate and UA are exclusive and so are BoD and BoA. And you really shouldn't count Shadowflame since you can't keep a good uptime on that DoT due to its CD.
Priests as a class have 4 DoTs: Devouring Plague, Shadow Word: Pain, Vampiric Touch and Holy Fire, but Shadow Priests don't really use the last one.
So I'd say we use the same amount of DoTs. Only one more if you want to squeeze in Shadowflame.

Remember: Haunt is not a DoT, it's a debuff.