Landlords should absolutely have the right to charge an extra fee for pet owners. As a pet owner myself, I realize the damage that can be done to a property I do not own.
These people are taking a risk by allowing pets onto their property, and many times, a simple security deposit just isn't enough to cover the damages.
If the pets cause damage, there's nothing preventing the tenants from having to pay up. But the truth is, most pets don't cause any lasting damage, and pet owners shouldn't be forced to pay extra because of this.
There are many cases where pet owners don't pay up, which eats up a lot of costs on the landlord trying to make up for it (for example, court costs). People also fail to realize allowing pets on your rental property requires you to have insurance to cover this, which is also why many landlords charge pet rent, and is a valid reason to do so.
Having a pet is a luxury, not a necessity (with the exception of valid service and emotional support animals). This comes at a cost. If you cannot afford all that comes with it, including pet deposits or pet rent if you do not own a home, don't get a pet.