Give me the Death Note, I can be trusted to act rationally. The only “undeserving” to end up on it would be people who step through Metro doors and immediately stop, even though there’s people behind them.
More seriously I know the author has said it’s about power corrupting, but if that’s the story he wanted to tell then he should’ve chosen a different protagonist. Its also a silly mantra, we do not live in a Tolkien novel, power isn’t some supernatural force.
i wouldn’t say that “old age” is a disease. it’s a state where actual diseases can kill you way easier, their incubation time would probably be lower than normal in that case.
but you could probably go for something like HIV which takes 1-10 years and might be fatal, especially if untreated.
After 39 days, you’re visited by your Shinigami, and can ask them for help workshopping how to phrase dies of some disease that can’t happen until they’re old so the auto-selected date is some point where they’re already old, but if they were already going to die before that, dying at their predestined time of an accident or disease is fine, too.