Ok, we have pets and some of them are really cute and/or worth having.
But wouldn't it be nice if it were possible to get a very, very rare pet.
Stray cats and dogs that would follow you and if you do feed them and shelter them, defend them from harm, they may befriend you and be your faithful, ever following pet.
Or you wander through the wilderness and all of a sudden you find this abandoned bear cub, or fox or wolf litter. All alone, maybe their mother has been killed and these little ones are awaiting a certain death, unless you start feeding them and looking after them.
These strays or abandoned animals shouldn't be easely found. It should be very, very rare and even if you find them, only good care can bind them to you. They shouldn't be exclusively in lower or higher zones. Any place in Tamriel is a possible place to find them. And never in the same place, so no looking for spoilers. Just luck and empathy for the animal can get you one.
It would set casual players and hard core players, newly started and seasoned players on the same level. Fair chance for everyone and in the case you get one and manage to keep it a realy special pet to show around.