You're right that death isn't a disease, it's an effect of disease. But aging itself is clearly a disease. When you get old, it's not like you're perfectly fine until you're age 80, and then you get struck down by a random sickness. The body itself degrades over time and loses various functions, like Lou Gehrig's disease.

I sort of agree with you, but a lot of illnesses are actually just vulnerabilities to certain other things. For instance, celiac is considered a disaease, but if a celiac patient never lets a grain of wheat pass their lips, they'll suffer no symptoms. As far as I know, AIDS won't kill you if you manage to avoid ever being exposed to any other infectious agent. A clinically significant phobia of spiders would not cause you any discomfort in a spider-free environment. Why couldn't we characterize "susceptibility to assorted causes of death" as an illness of its own?

Not being immortal (in the sense of dying from old age) is obviously an illness

Is the set of all possible fatal illnesses itself an illness? I don't think so; that just seems like a type error.

The explicit cast provided avoids that problem.

It seems reasonable to describe ageing as an illness, particularly the symptoms that can be traced to a specific (and currently universal) biological flaw in cell reproduction.