There are different scenarios in the life of your cat where you might need a small cat litter box.
Many cat owners like to start with a small cat litter box for their kittens. Kittens learn faster to use a litter box when the stepping-in and getting-out happens easily. Many of the available models offer a lower side for easy access.
Older cats might prefer for the same reason a small cat litter box too.
Cats are clean animals. They groom themselves constantly, not only after they go to the cat litter box. They bury their waste with litter and afterwards they clean themselves. Continuous grooming is in their nature.
A research found that cats groom themselves about 50% of their waking time.