They said in multiple interviews that adding pets and mounts is something they’re trying to do, but there’s some engineering complications that’s in the way. They said the same thing about having your other characters in Follower Dungeons.
I know it sounds simple, but the Pet AI is coded around the character, and detaching it from the character causes all kinds of glitches. They would need to replicate the creature and name, and then give it its own pathing AI to wander around, and that’s difficult when you have to factor in the nearly infinite possible layout’s of a person’s house.
Mounts are a little easier, as they’re static creatures everyone has access to, but there’s a reason that the Garrison Stable had your mounts staying perfectly still.
Trying to make Housing itself work and something like this would be an engineering nightmare. So they’re doing one first, then the other. They’re struggling to get the PTR online right now.