Eliezer it's a good question and a good thought experiment except for the last sentence, which assumes a conservation of us as subjective conscious entities that the anthropic principle doesn't seem to me to endorse.
You can also add into your anthropic principle mix the odds that increasing numbers of experts think we can solve biological aging within our life time, or perhaps that should be called the solipstic principle, which may be more relevant for us as persisting observers.
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Don't get bored with the small shit. Cancers, heart disease, stroke, safety engineering, suicidal depression, neurodegenerations, improved cryonic tech. In the next few decades I'm probably going to see most of you die from that shit (and that's if I'm lucky enough to persist as an observer), when you could've done a lot more to prevent it, if you didn't get bored so easily of dealing with the basics.