CDS has a 12s duration and a 15s cd unless it has been changed since I last did testing or WoWHead and MMOChamp are wrong.
How is it "quite obviously not as intended"? Are you implying that the pet duration and the pet buff duration is the exact same by complete coincidence? I suppose that's possible, but it seems incredibly unlikely to me. Keep in mind these people have designed the most successful MMO, and arguably video game, in history. Do they make stupid decisions at times? Yes. Are they stupid? No.
It being a "terrible design" is definitively an opinion. Alot of people agree with you; I personally think it's only moderately annoying, and wouldn't complain at all if DE were simply instant.
If you actually read my post, you would see I never defend it as good design. In fact, I say several times it isn't. All the post was saying was the the developers are not stupid, and when several interactive abilities all line up to have the same cooldown, you can probably assume that wasn't on accident.