The pet deposit is for the damage you expect done by the pet in excess of the human.

Sure, I agree with charging a separate pet deposit. But a lot of times it's just a fee being called a "non-refundable deposit".

Because if you can’t find a landlord with more generous terms.

At least in my area, it just seems like a standard charge apartments do now. If anything, corporate rental properties seem to be charging these fees more than landlords. Private landlords either say no pets or just have a larger deposit. Which indicates that it's about generating additional revenue for these corporations, not purely covering pet damage.