I've only been around to see three kittens acclimate, but I've always been surprised at how quickly all of them start using a litter box, especially compared to the toilet training time for puppies.
What makes cats so quick to recognize and choose a litter box to defecate into?
I will accept an answer with a convincing reference.
I think it has to do with their instinct. They feel that when they have to go, they have to go to a soft soily area and that's what the litter box replicates (remember that cats like to cover the area with dirt after they finish??). In the house, there is no other area like that so the litter box is the first place that they will go to.
It is important for a cat to hide its smell, because a cat is a predator, and if the cat's smell is not hidden, its prey will be alerted and harder to get. But the cat is also prey for other larger animals, so it makes sense to hide its smell from other animals. This is the basic reason for cats to hide its smell by burying its poo.
Ten months ago I adopted a feral cat (yes, a wild animal,the vet says he is at least ten years old.) It did take 3 days before he started to use the litterbox. This was mostly because he was terrified of me and my apartment and it took some time for him to get used to things. So most cats learn to use a litterbox very quickly no matter their age.
All cats have an instinct to hide their waste from prey and other predators. Domestic cats are (mostly) descended from African wildcats, which further refined that instinct to burying their waste in sand. Kitty litter is specifically designed to mimic sand and thus trigger those instincts.
Note that if there is something wrong with the litter box, pain from a UTI or other stress in the cat's life, they may find other places to go, but those places will still usually be fairly soft and loose (e.g. clothing or bedding) to fulfill the core hiding instinct. Unfortunately, those are usually also the places that are most difficult to clean and most upsetting to humans.
Other species of cats (including some used in "hybrid" breeds) prefer to hide their waste in water, dirt, leaves or other materials based on their habitat, though some can be trained to use litter. Likewise, some housecats can be trained to use a toilet. However, in both cases, the training is difficult and fragile because you're working against their instincts rather than with them.
In the wild, house cats who are lower status in their clowder will bury their waste so the aren't percieved as challenging the alpha's right to that space. Humans are just taking advantage of this existing behavior
Dogs, on the other hand, view toileting habits as another way to announce their presence to the world.
