I'm not sure I understand. If existing humans became immortal, but no more humans were created, then it removes the need for a future extinction to explain the number of humans that will ever exist.
It's not about the number of humans. It's about the number of observer-moments. Imagine if you were the only human ever. If you're only twenty years old, it's unlikely that you'd live to be a billion. You're not going to just happen to be in one of the first twenty years.
A self-modifying AI is built to serve humanity. The builders know, of course, that this is much riskier than it seems, because its success would render their own observations extremely rare. To solve the problem, they direct the AI to create billions of simulated humanities in the hope that this will serve as a Schelling point to them, and make their own universe almost certainly simulated.
Plausible?