Hotels discount rooms all the time for guests they know have a very low likelihood of causing damage. The probability of a person with a pet causing damage must be sufficiently high that it makes sense to charge extra. There's plenty of competing landlords and hotel businesses, and if there was economic opportunity in doing it the way you said, it would be done.
It's not just pets though. Hotels will charge more for wedding parties, who are far likelier to cause noise complaints, damage etc, than a crew of workers who will be sleeping, going to work, rinse repeat.
Oh, I realize why landlords prefer it. I just don't think it holds up under scrutiny. If you're my tenant and I charge you $100/month for dog rent on your new puppy, who causes $0 damage and lives for 14 years, I've extracted $16,800 from you, $0 of which will go toward rehabbing the apartment of dog damages when you leave.
Additionally, a landlord will want to work on the space more often than once every 14 years. A security deposit does not cover this.
Additionally a tenant renting for 14 years is making a suboptimal financial decision regardless of pet ownership. Much more than $15k would be unnecessarily spent, for many people. A tenant who wants to get the better end financially, especially a pet owner, will buy or at least keep the landlord honest about market costs of the rental.