This is a unique capability for Hunters. Who hunt and stalk their pets and tame them.
Warlock and DK pets are “designed” pets. The while Demonology experience with pets, the Tyrant, the imps, and the deathstalkers – that’s unreasonable to be able to try and train that up.
I’m perfectly content with my non-stylish, all the same Warlock pets. Adding in a new pet dynamic would just be a lot of effort for little game, both in bottom line stats and numbers, and just overall play value.
If I want a menagerie of pets, I’ll pets from the wild, I’ll roll a hunter. Lets hunters be hunters.