Cats do not pee/poop in holes or caves in the wild; they "go" out in the open, where they can see potential threats coming. They cover their "stuff" so preditors can't smell where they've been. While covered litter boxes are great for us people (less mess, don't have to look at it etc.) they are stressful for cats, and often the cause of them not covering up when they're done. A good litter box is one that is open, at least 1 foot away from walls and has two exit paths. I noticed Wayfair has a good open top, high side box on sale.