I don't think a social problem (that will be solved in time, and is already solved in some countries) is a reason to prevent this from happening.
Social problems can be fixed, death is final. If euthanasia doesn't become legal before, it certainly will be after.
Much has been said and written about the cruelty of immortality, since the myth of Sisyphus and probably before.
“The Mortal Immortal” is a story about prolonging lifespan but not healthspan, and also not emotional fulfilment in life — https://en.wikipedia.org/wiki/The_Mortal_Immortal. There are also TV shows (“Altered Carbon”, “Black Mirror” USS Callister and other episodes, “Twilight Zone”) and video games (“Nobody Wants to Die”) about it.
What your parent comment speaks about (the vanity of endless life) is particularly explored in Bernard Williams’s “The Makropulos Affair”. Endless life could mean no regard for quality of life and endless trivial pursuits.