I think there are many people out there who would have chosen euthanasia if it was an option. The way the laws are written in most places, a family member assisting someone's death is committing murder. You have to be completely willing to sacrifice your life to assist a loved one in dying. Personally, I would far rather face euthanasia than a life in an iron lung. While this is not a huge issue these days, there are people who wish to die, and cannot do it themselves.
As for myself, if I had an Alzheimers diagnosis, I would enjoy the time I could spend with my family while I was still relatively healthy, prepare them for my passing, and end it before the disease progressed to its natural end. I wouldn't want to feel the dissolution of my personality, and leave only ugly memories for my family.
I think good pallative care, counseling and support are necessary for those suffering. In many cases, pain management and counseling can change a person's outlook on death and dying. It is not always the terminally ill who wish to end their lives, but those whose chronic suffering, with illness and disability who can't face the life they must lead. However, in the US at least, we aren't very good at getting counseling for those who need it, and we distrust pain management because it is so often abused. If we were better at dealing with the anger, frustration, depression and desperation of the chronically and terminally ill, we probably wouldn't be discussing PAS or euthanasia.
That being said, a person in their right mind should be able to end their own life. If they cannot do it themselves, they should be allowed to sanction another person to do it.