The sheer size of pet pens makes them a real issue to keep thieves away from them - particularly for leveling players or solos who don’t want a giant base footprint. Putting even a basic t1 structure around the lowest pet pen is like shooting flares into the sky announcing your location.
It would be awesome if there was a single pet taming option such as the stables for people who don’t need to be taming multiple animals at once. Given the stables are a thing, I really don’t see how this wouldn’t be possible, or any reason not to. I think most people agree the sheer size of the regular pet pens is annoying.