Vikram Seth does the same thing with the ending of "a suitable boy" as does Anne Proulx in "the shipping news"
Writing of one's own mortality in these situations obviously invites the final word, but it actually doesn't have to be cast as such.
For this author the situation is terrible, but the writing doesn't have to echo that finality, there's a choice to be made.
To the individual, here is, in effect, never enough time. There never will be.
From evolution’s point of view, individuals are only a bundle for the survival of genes. It is no surprise that we want more, hence society.
For society, one could argue that its core principles (liberty, freedom, security, flourishing, pursuit of happiness, shared narratives, etc.) are only provided to each individual in a time-bounded way. Individuals may be heartened when they have confidence these principles will carry on to the next generation.
I like this and care deeply about what happens to our world after I am gone, but I worry (excessively, actually) that most others do not. Greed, immediate gratification, etc, these things cloud our judgement so greatly that even I have trouble remembering that the future exists with or without me in it.
It's an interesting problem to think about, but I have no idea what branch of philosophy it falls under, so pardon my sophistry. I do wonder, though; how do we get people to care about this?