I'm not sure I want to grow particularly old. Slowing down is okay, as is the experience of years and all that. The bit that worries me is the bit where your body stops working properly. You're no longer self-sufficient, you're often uncomfortable or in pain a lot of the time, and in the worst case your mind is no longer working properly, either.
Medical care helps, obviously, but it also seems to draw things out. Maybe it's better to let your body shut down when it wants to, instead of convincing it to hold on against its will?
It seems to me that the animal kingdom might be a good place to look for the right way to grow old and die. You don't see many completely geriatric animals. Old, sure. You do see arthritic, stiff, slow-moving animals sometimes. However, I suspect Mother Nature is a little less forgiving than human medicine. The animal way looks a lot quicker—you might get sick and die, or get eaten, or just freeze to death, but it doesn't seem the case that an animal will hold on for years, senile and unable to care for itself.
I'm not suggesting we should force our old to fend for themselves, nor am I suggesting euthanasia (although I'm not not suggesting it, either.) But maybe there's something in the idea of accepting death more easily? Everyone makes their own choices, but when I see death coming for me I think I'd be inclined to say ‘I'm not going to run away.’ Avoidance just stretches it out.