I've read most of Card's stuff including the Worthing saga. IIRC, the twist was that the telepaths had been doing the healing for so long that no one alive remembered what pain was like so when the telepaths stopped, there was a major backlash. Overall, I didn't enjoy it as much as the Ender and Alvin Maker series. I felt he was trying to make the point that there are "reasons that God doesn't intervene when he has the power to do so even if we don't understand them". A little too preachy for me. He had another story (Lost Boys) that did the same thing.
Regarding the puzzle box, my first thought was "Dinosaurs...big fecking dinosaurs, the human race needs some more predators running around to put things in perspective". Then the paranoia set in. "Who the hell else has one of these things?!? and I pushed the second button and all the boxes were gone that ever existed now or in the future. I wonder what historical figures would have done with such a device? Say if Ghandi, Oppenheimer, or Tesla were given their own 5 button box.