Part of it is the time-consuming nature of asking everyone for their ID.
Another issue is that, with a paper ticket, even if you shared it, only one person could use it at a time nonetheless. With etickets, you could make multiple copies, hand them to several people, and as long as two people weren't on the same train at the same time, the system wouldn't be able to recognize the abuse.
I know Amtrak is nowhere near ready for this technology (and it probably wouldn't be worth the investment), but it would be nice if there could be some kind of card similar to a transit smart card, where the pass is stored on your card. If you lose it, you pay a small fee ($5-$10) and get it replaced, and the old one is cancelled and the pas automatically transfers to the new one.
Again, though, the market for such would be very small on Amtrak. I don't think the conductor devices are equipped to read smart cards, but if they were, it might even be doable through an agreement with a credit card company to use a smart chip enabled credit card.