Is this the sort of thing that the government should be regulating in principle? I don’t think it is. (But then, I do tend to lean libertarian.) Plus, it seems like it would reduce the supply of and increase the price of housing.

I think it might increase supply, but only in a paradoxical sense. I’ve had to deal with tremendous damage done to my home by line of our pets, and I’ve only put up with it because the animal responsible was incredibly dear to my wife. If I was renting the house out and had to deal with similar damage done by some stranger’s pet every time the house turned over, I think I’d throw in the towel and put the house up for sale. It’s just not worth it.