because simply making all existing humans immortal solves the DA as well.
I disagree. An appreciable number of people might be the ones designing the AI, but they won't spend an appreciable portion of their lives doing it.
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.
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?