"There was a valid purpose for keeping cats hundreds of years ago when rats and mice abounded but now?"

"Yes, cats kill critters, and thank heavens for that, otherwise we'd be overrun with squirrels here. The two years between cats resulted in us having to re-insulate over the garage, fish a trapped weasel out of a wall, trap an endless stream of deermice and house mice, and we still have a bat problem (the cat's just six months old)."

I am in full agreement with the sentiments expressed and implied above. There are reasons that we are not over-run with varmints. Have you ever seen an underground rat 'city'? Fascinating and precise but not pretty in its implications.