Of course insomnia is seen in Alzheimer's patients in nursing homes, and of course caregivers will administer drugs to help treat some of the symptoms of Alzheimer's, including insomnia.
But we were talking about curing Alzheimer's with improved sleep.
I've never heard of a documented case of curing/reversing Alzheimer's with a sleep aid.
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I repeat:
Sleep aids (sleeping pills, anti-anxiety drugs and anti-depressants) help patients get to and maintain restorative sleep.
Many Alzheimer's patients are using sleep aids.
Therefore, if your sleep theory were true, it would have been seen many years ago in nursing homes, and advanced as a possible cure for Alzheimer's a long time ago.