Humanity might have never left the prehistoric times. Dogs helped with guard, hunting and other things. Cats, I'm not so sure about what they did, although probably rat catching so diseases would be more rampant. The Black Plague for example was much worse in countries that killed cats because they thought cats were to blame, althoug cats actually killed the rats, that spread the disease.
That's exactly what they did, I have three of them for just that.
I live in the country in the first time I moved out here the first winter there were so many mice I mean it was just insane, I got three cats now they annoy me laying on the vehicles, they've laid on one of my trucks so much that they took all the paint off the windshield wipers. And constant paw prints. But for a few handfuls of food a day they keep, rats, mice, snakes, and rabbits away.
During the daytime they'll lay in my garden and kill rabbits as big as they are.
The value of cats is not truly understood or appreciated until you live in a wooded area.
I have not had one mouse in this house.