The rats that the cats are keeping out of the stores are a much larger source of pathogen transmission to humans than the cats are. Not only do rats carry many more dangerous diseases than cats, but both can also transmit toxoplasmosis to humans. As it is transmitted through contact with feces, from which of the two are you more likely to encounter feces spread all over the store?
So, while I actually find both rats and cats endearing, I'd take the cats over wild rats in the stores any day.
I think we owe our civilization to cats - without them we would have never been able to stop being hunters-gatherers and settle into agricultural society as having food stores would have been impossible due to rats.
And Black Death, owing to Church persecution of cats, is another great illustration of cats' role.
Cats were not widespread in the ancient world until very late. Herodotus writes about cats as an Egyptian novelty. People had mass food stores long before then.
"But recent genetic and archaeological discoveries indicate that cat domestication began in the Fertile Crescent, perhaps around 10,000 years ago, when agriculture was getting under way."
Edit in response to the comment below as i hit post-limit:
"Housecats seem to have been extremely rare among the ancient Greeks and Romans;[16] the Greek historian Herodotus expressed astonishment at the domestic cats in Egypt, because he had only ever seen wildcats.[16] Even during later times, weasels were far more commonly kept as pets[16] and weasels, not cats, were seen as the ideal rodent-killers"
Even if we assume this is correct and Herodotus and others were simply ignorant of this, it's obvious that the Greeks of his time, including those in Anatolia where he lived, where food had been stored in massive quantities for centuries if not millennia, did not have cats.
So, while I actually find both rats and cats endearing, I'd take the cats over wild rats in the stores any day.