@Nick, thanks for the comment. That is strange that most of your rentals don't accept pets. If landlords did that in Austin, they would not find a suitable tenant for a while. Some management companies here require a non-refundable deposit, while others don't.
Jordan, most rental properties don't accept pets here and the one that do cover potential damages by requiring a larger non-refundable pet deposit. Aggressive breeds are a usually not accepted. Like your advice of removing carpet...no brainer!