She has many towers and beds, but her favorite spot is a pile of old cardboard

Is that a lilac cat?

Cardboard is a good insulator, it absorbs moisture and its smell is likely to be instinctively associated with safety. Cardboard->wood->trees, a good place to take a nap without getting disturbed. And I bet that paper shares some qualities with leaves too, it sounds and feels similar when walking over it. She knows what's good!

Cardboard has mystical powers for cats, is my conclusion. Also a very satisfying thing to bite!