Cats like keeping thesemlves clean through constant washing. Many cats also like being brushed by a human, but since humans can’t cater to a cat 24/7, and other people can’t take over just to keep your cat happy, you have to find a better alternative.
One such alternative is a self-grooming brush that you mount on a wall or place on the floor. Now your cat can rub against the brush and groom themselves. It’s not quite as good as having a human servant do it for them, but it’s the next best thing when you have to leave your cat alone.