The main issue with the paper tickets is that they predate electronic processing so they are intended to have value themselves. The conductor doesn't have to check that the piece of paper is valid or not; that's why they're printed on tamper-resistant paper.

Airlines can do electronic ticketing because every airport has staff and a computer to scan the boarding passes to ensure they reflect a real, unused reservation. Amtrak, unfortunately, doesn't have this. Even if the conductors had some sort of scanner, they'd require a constant data link to Amtrak HQ which would be difficult and/or expensive in many areas.