> Rat traps are less expensive, more effective, less prone to killing things other than rats, sanitary, don't have to be fed, don't need a litter box, don't cause allergies, don't need shots, medications, or vet visits, and don't have kittens. Far lower impact and much less work than a cat.

Are they? If the cats are eating rats, then they don't really need to be fed. If they're allowed to go outside, then you might not even need to clean the cat's litter box. Rat traps have to be reset, and the corpses disposed of; cats do all that automatically.

Yes, they are, objectively. The minimal amount of labor involved in setting and clearing a trap (literally 30 seconds) is significantly less than the time spent tending to a cat. Even if you only pet it occasionally. I own traps I don't even have to touch with my hands. And they were inexpensive.

Rat traps work 24/7, unlike a cat which sleeps up to 16 hours a day.

Cats must be spade or neutered, an additional cost and effort lest they contribute to the epidemic of semi-feral cats.

Outdoor domestic cats kill an estimated 7 - 26 billion wild animals yearly, most birds, 3/4 of which weren't eaten when studied.

Outdoor cats especially need flea treatment, else they'll bring them into the building. Having dealt with a flea infestation, trust me you don't want to. Involves poisoning your whole dwelling for a few days at significant expense.