Why on earth do people (you're not alone, I know) prefer to assume that direction of causation, rather than that the underlying condition that leads to Alzheimer's causes sleep disorders too?
It's well known that sleep disorders are associated with other neurological or mental disorders.
I think there is a pervasive disease of thinking where people associate science and smart people with counterintuitive statements, so every obvious relationship gets inverted.
And can you answer the basic question of why sleep is even necessary at all?
Lack of sleep is eventually lethal, and I read a very interesting study a couple years ago that seemed to have a plausible mechanism and stunningly reasonable methodology, but I haven't heard anything about it since then. So I still don't know if it was fake or something, because it seemed like it should get a Nobel Prize. Although it used fruit flies so perhaps it didn't generalize.