Yes, it's good to have the emotional support of a wife when you're in declining health. You can get that from family and friends, though, and from church involvement if you're into that. And if worse comes to worse, you can always hire a cute home health nurse and turn your life into a Benny Hill skit. (Not meaning to be insensitive here. I hope you're not in the position you're alluding to.)
Unfortunately, I've known plenty of men who were divorced by their wives after they became ill in mid-life. Spouses do not necessarily stick with you, when the going gets tough. I'm sure men leave their wives sometimes in this situation, too, but women initiate divorce much more often than men do, so I think it's the men who are more often left holding the colostomy bag.
I think it's another reason older single women aren't interested in relationships: they don't want to end up being the caretaker to an ailing man. Women are blessed with longer life expectancies, and they also tend to pair up with men who are older than they are. For example, a 60 year old woman might be looking at a 65 year old guy, thinking, "Do I want to get involved with someone who I might have to end up being a nursemaid to in the next decade? Do I want to end up feeding this guy oatmeal and wiping his butt?" Naturally, that dims their romantic drive a bit, lol. Many women have already spent a good chunk of their lives taking care of other people -- their children, mostly, but also, in their minds anyhow, their ex-husbands, and so they don't relish the idea of doing more of that in their later years. I don't blame them.