Well, let's look at this in a real world kind of way. How many people do you know who actually own a bengal tiger. Or how about owning a Rocky Mountain timber wolf? Or a full gorwn grizzly bear? No one. And you knwo why? Because they are wild animals and that makes them very dangerous. And even if you could get one, which is difficult but certainly not impossible, you would have to provide a natural habitat of some kind. You can't have a wolf living in the house, or a bengal tiger curling up on you in the middle of the night.
It works the same with paracritters. ALL paracritters. Blackburry Cats and Tallis Cats might be able to slip through the cracks simply because they are so mundane in appearance most of the time. I could even see a Gabriel Hound (maybe) being kept as a pet if it was taken early enough. But you always run the risk of having one of these critters freaking out and going for your throat. Any company/government who uses these things does it with handlers, not owners.
Just keep it in mind that if you let any of your PC's get something like this that they don't live close to anyone else. Trying to get a hellhound into an appartment is nothing compared to trying to get out once the building is in flames.
Gabriel
PS - Blackburry Cats tend to pick who they want to live with, not the other way around.