Well, there is the question of paying for the nursing home. The sad reality is that the options offered by our social safety nets at lot less attractive than the options available if you can pay for it.
Unless you are completely out of it to the point of not caring, at which point your loved ones may still care though.
Separately, optimizing for being able to pay out of pocket for a top tier nursing home seems like a strange life goal to me. Maybe people really do have that preference, but it looks to me like a lot of people in the greater "personal finance" hobbyist world just like saving for it's own sake. Nothing wrong with that of course, but the sanctimoniousness of this group is a way over the top IMO.
Being able to afford a comfortable life after I am literally too infirm to work is the vast majority of the reason I continue to want to earn money. I'd be really interested if you could persuade me that I am misguided on that!
You are now 60 or 65 or maybe even 70, you're slowing down some, but you aren't too infirm to work. You have a fair bit of savings.
Do you:
1) Keep working until you can't work anymore
2) Retire, but live frugally so that you can be sure if you make it past 95 and need skilled nursing care you'll be able to keep private paying for a top notch nursing home.
3) Build out a retirement budget that assumes you won't make it past 95, make the absolute most of the next decade or so of relatively good health (hopefully!)? Go take that trip you and your wife always dreamed. Lavish your adorable grandchildren with gifts that certainly don't need. Fly business class instead of squeezing your old bones into coach.
Keep in mind that if nothing else you'll still have social security no matter how long you live.
Granted this is somewhat exaggerated for effect, but there's a difference between taking the worst case scenario (a funny way of referring to living a long time) into consideration and letting the tail wag the dog.