Or small feathered animals. Because they tended to thwart hunting, the bells could also discourage domestic cats from wandering.

Considering how much more expensive food used to be, allowing pests to run rampant and get into the food stores seems unlikely. Although, I believe they were more likely to rely on dogs to kill rats.

I'm guessing it was more about stopping the cat from getting worms

Also possible they wanted to reduce the number of small animal carcasses to clean up, whether from the doorstep or interior of the home. Cats love to bring these as gifts to their keepers.