I think landlords should assess on a case by case basis, rather than having blanket rules. I have owned cats (inside and outside) and rottweilers (outside only) and never had an issue. In fact, every property has been in better condition when I vacated than when I rented it.
My first property I got two cats without asking not long after moving in. A few weeks after that, my ex decided I could have my rottie back. Then 3 months after that, my new boyfriend (now dh) moved in with his rottie. The landlord lived interstate, but a couple of months after all the animals moved in, he called over, apologizing for the intrusion and asking to see something that had been an issue at the back of the property. I apologised for all the animals, but invited him to inspect how we looked after the property with them here. After looking around, he was more than satisfied, and when we vacated 2 years later, he wrote me a great reference.
I would also be willing to pay an extra bond when renting to cover the animals. Is there such a thing as a "pet bond"?