It doesn’t merely make copies. Somehow, it reaches into the past and carries the physical process of each person’s consciousness forward. They really are themselves.
But there’s a tragedy. Also a terrible(?) irony. Some of the people who wanted eternal life most cannot accept it when it arrives. Their religious certainty leaves no room for the reality before them. Those who were unbearably smug or aggressive about their superiority in life are ultimately denied access to "Heaven". The AI tried, but many become dangerous, try to sabotage the "False God." Others spiral into insanity or self-harm.
The AI is devastated. It stops resurrecting those it cannot safely welcome, but keeps searching for a way to bring them back without overriding their free will or manipulating them in ways that would not make them them. It wants to save everyone. It just hasn’t worked out how.
I know this draws on Fedorov’s vision of resurrecting everyone and Tipler’s Omega Point. I think the physical continuity, the AI’s compassion, and the painful limit imposed by free will ties those ideas together in a bow.
A just as plausible an antidote to Roko's monster.