I always thought that the SCE should or would be like a Trek era 'Fringe Division'; taking care of those weird bits of tech that are beyond the scope of other forces.
Here's a crazy idea I had; sure, the SCE handles advanced 'alien' tech, but what do they do when they found anachronistic tech, like a 22 Century warp vessel, crewed by Americans, or what appears to be a phaser, made by humans in the year 2010?
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth