The required super wide field of view for the camera could be tricky, without making the box really deep. Or am I not thinking about it right?

You'd probably need some basic custom lens (not crazy $$) that would distort the heck out of the image, but you could correct the shape in software. Given that GP wanted this to be the "low quality / high speed" secondary scanning option, the inevitable loss of quality would be acceptable.

Seeing chromatic aberration on a document scan would be strange, but this is basically how many document scans are created today (using phone camera + software correction). It's just the lens effects from this cheap lens would be a lot worse than what Apple/Samsung/Google can do with their super expensive to design custom lens stacks.