My cat uses a litter. She always buried her faeces until fairly recently - why? Cats bury their faeces to prevent the smell drifting around the area. Cats don't want the smell drifting around signaling their presence because they want to act in a low profile way by being subordinate to the boss cat, the human "owner".
Domestic cats know their place on the world and it is second to us. Although a lot of humans in return don't see cats as secondary to them (me for one). Cats feel subordinate because we feed them. We dictate their means of survival. Everything turns on our activities towards them. They need to keep the balance and ensure that we humans think that we are the boss (although you wouldn't think it sometimes). The cat needs to remain subordinate to get his food, he thinks.
If a cat stops burying faeces it would usually mean that he or she is the top cat who wants her smell to waft around the place to alert other cats to her presence and to be aware of her status.
And I think this is happening with my cat. I treat her totally as an equal. I don't see her as a cat in fact. I have done that for the past 14 years or so. We have a great understanding. She is very relaxed with me. She has no worries about being subordinate to me because I have trained her through my actions that she is not subordinate.
Accordingly she no longer buries her faeces. That's my theory anyway.