Cats were domesticated by humans to kill mice and rats in our grain stores and primitive barns thousands of years ago. Cats by their very existence should be eating mice and rats. They like all other felines are obligate carnivores they not only have no need for vegetable matter it is harmful to their digestive health. We had barn cats growing up they never once got feed by us the lived exclusively by hunting in the barn and afield. If too many were a round we would set out traps and catch them with raw meat as the bait.
A friend who knows more about cats than I do said only 25% of cats will go after rats. I guess the rest are scared.