The Good: Uploading Consciousness
You can kill Jor-El's body, but you can't stop him from uploading his consciousness into a USB stick with an "S" on it (excuse me, with the Kryptonian symbol for "hope" on it). No idea why Lara didn't also upload her consciousness, but regardless, Jor-El's "digital immortality" was a cool idea, with some real scientific merit. "Whole brain emulation" has been a major goal for scientists for decades, and has gained momentum in recent years since Russian patron Dmitry Itskov spearheaded an eclectic, international community of scientists, scifi enthusiasts, and even spiritual leaders looking to solve this problem (the problem essentially being death. It's a big one!).
Foremost among them is the controversial author/inventor/Googler Ray Kurzweil, who believes the technological singularity (when artificial intelligence surpasses human intelligence) will be reached by 2045. The growing fields of brain-computer interfaces, quantum computing, and neurological modeling have generated numerous theoretical approaches to backing up a human brain. Granted, we have a long way to go—we've barely scratched the surface of human consciousness, let alone figured out how to copy it digitally. But as the great rocketeer Robert H. Goddard prophetically said, "the dream of yesterday is the hope of today and the reality of tomorrow." We may not be able to manifest ourselves as Russell-Crowe-holograms, but some form of digital immortality is likely to emerge in future decades.