Actually, they do, Varamyr Sixskins stole most of his companions from other wargs. Like with dragons, being a warg would be being a "dragon rider", while having a pet, like Robb or Jeor Mormont would be having the animal as "friend". And about the clutter, that's why I only suggested Dire-wolves, not many of them around

And yeah, they wouldn't live much, even though we do not know how long is a dire-wolf's life-span, that's why breeding them and actually instructing them would be important.
I meant tame as in the dragon taming mechanics, comparing it to the owner getting inside the animals body, not as in simply owning a pet.