Seems very naive to think that people who have access to immortality technology aren't going to have children, and if you're immortal of course you're not going

Seems very naive to think that people who have access to immortality technology aren't going to have children, and if you're immortal of course you're not going to watch your children grow old and die, so you share it with them. I leave it as an exercise for the reader to count out how many generations you need to run this until it's 'oops, all self-replicating individuals with broken off switches.'