To say that death is a 'part' of life comes from the religious impulse that offers humanity an afterlife. Therefore, life and death form a cycle. To this end, death is a part of the goodness of the natural, theological order.
But to deny the existence of god is to also reject the possibility of an afterlife.
This is why Wittgenstein commented that death is a termination of life, not a part of living for which we somehow prepare. His obvious referent her was Heidegger, who wrote that being in life is being headed for death, etc...my pont here is that, regarding death, there's been a secular counterforce around for the last 100 years or so that says death is dad.
We can also affirm the medcsci has always sought the prolongation of life. It likewise has always formed a marriage of convenience with religion to offer people a backup consolation when medicine fails, as it always, finally, does.
As for children, simply raising them as atheist (as I did) will take care of the 'death is goodness' issue once and for all. Conversely, raising them as religious and giving them this book will create confusion and ambiguity.
That being said, my personal view is to wait to answer hard questions only when they're asked, which obviously gives the parent an indication that the kids are ready to understand. My reply to my own was, "No one knows what happens after you die. We have doctors whose job it is to make sure people live as long as possible". So my opinion tilts toward Barathon's: giving a child a book about death is a really bad idea.
Lastly, no, the indefinite prolongation of life is not realistic; med sci process is by increments. Moreover, the huge steps in life's extension have, historically, come with improvements in social sanitation and available vaccines. Cytology, organ transplants and pills for diabetes are fun to talk about, but are, statistically speaking, only a drop in the statistical well.