I'm not sure that I'd want to burden my family with my old-age care, I'd rather they lived their lives to the fullest than had me as a millstone around their necks preventing them from achieving their dreams. If I was ever incapacitated in a way that required 24/7 care in my old age I'd far rather make a dignified exit and have my descendants remember me by doing something meaningful to them than waste time and money on me when I'm too demented to even appreciate it.
Of course, this will always be a deeply personal decision and there's no universal answer to this question.