That is, it's not the dead that are in pain, it's those left behind.
So, while I agree with you, it doesn't seem much worse than death, especially if the family accept/believe that the Alzheimer's patient is actually not suffering.
For example, if my dad lived long enough and ended up with it, had I been convinced that he actually wasn't suffering, it may be less heartbreaking as his son (but still heartbreaking for my personal loss of the relationship with my Dad, and him not knowing me).
It's hard for me to say, having not had someone super close end up with it -- only more extended family. So those closer/more affected may have other thoughts.