Having watched my father and father in law approach the end of their lives, I am inclined to think that the falling is a symptom of the infirmity rather than the cause of death. Where medication messes with the electrolyte balance, and many of them do, the ability to maintain vertical hold simply fails.
My father had all his marbles to the end, had battled colon cancer and recovered from 2 serious strokes in his fifties. When he was admitted to hospital and then transferred to a care home because he could not stay upright (and my stepmother could not get him back on his feet when he fell) he basically gave up the fight to survive and was dead within a week. My father in law had increasingly bad dementia for the last 10 years of his life and survived for three years from his admission to hospital following a series of falls. In the end his heart failed.
Neither of them died because of the falls. They both died because they were old.