I used to work in property management and we charged extra fees each month for pet rent. I initially was against it when I started working there, but by the end I completely understood why they did it.
The reality is that animals are rougher on homes than humans are. Even things like the backyard will have more wear and tear on it with a pet than with humans and all of this has to be dealt with during turn over.
A perfect example of this is paint. During a normal turnover we would do a "tier 3" paint job. Which is to hire someone to come in with a spray gun and spray the walls white. They don't target baseboards or ceilings, but the overspray will generally cover some of it (ever notice how apartments and rentals generally have white walls, white baseboards, and white ceilings?). It is a cheap and lazy paint job that we have negotiated flat rates for $300-$400 per home. This happens no matter what.
But on a home with a pet occupant, it is nearly guaranteed that you would need to perform at least a tier 2 paint job which is generally coupled with a carpet replacement. The carpets are torn up (or peeled back if they are recoverable), the painters come in and spray the walls, baseboards, with overspray on the underlayment (under the carpet) and the ceiling edges. This usually runs us $800 - $900. So pet rent usually goes to that.
After a tier 2 paint job, a carpet contractor usually comes and re-stretches the carpet and does a carpet shampoo. But on a home with a pet occupant this has to be replaced since hair and dirt that most people don't notice, can cause allergies for the next tenant. So with a pet occupant our turnover cost goes from a standard $200 for re-stretching, as much as $1,200 for fresh carpet. Pet fees go to that.
A final turnover item is the backyard. Normally a lawn care company comes to do a standard touch up on the yard. This includes mowing, trimming, leaf blowing, etc, just to make the home presentable for walk-through. But with a pet, the grass is usually thinner after the pet use, and needs some re-seeding. Sometimes it is destroyed with holes or previous renter patches. Fences often need fixing (which gets really expensive, even if it is just a few boards) and so on. A standard lawn turnover usually costs $50. But with a pet it usually is $100+ and I have seen extreme cases where it is in the thousands.
This all comes from someone who owns a big dog that I love. My dog is well behaved. He never has accidents in the house and for the most part doesn't cause noticeable damage. But there are minor things that you just don't notice that I have only seen now that I have experienced it through property management.
Pets really do cause more wear and tear on homes than human-only occupied homes. That is why there are pet fees. They know that more is going to be done when you move out and those fees contribute to limiting that.
Now many renters have learned that if they claim that a pet is an emotional support animal, that they can avoid pet rent. But the reality is that if you claim a pet as an emotional support animal, that you can basically kiss your deposit goodbye. The company that I worked for was pretty good about giving back deposits. There was a $400 non-refundable deposit that we collected upon move in that you never got back. THis covers standard turnover stuff like tier 3 painting and carpet re-stretching. So if you leave the house in good condition, then we can give you everything other than that $400 back, and usually did. If you have a pet, then the extra rent from pet rent is calculated to cover the upgrades to tier 2 paint jobs and carpet replacement jobs. So again, you get your deposit back unless something is beyond normal wear.
But if you avoid pet rent with the emotional support animal, then that is fine. They won't charge you pet rent, but you will certaintly not get any of your deposit back. The owner or property manager still has to do the carpet replacement, yard fixes, and extra painting regardless of whether you pay pet rent or not. So emotional support animals generally lose their deposits to cover these costs, while people with pet rent usually get their deposits back.