I think the most important point is that it's slow, it involves many people, and leaves a physical trail. These are all advantages for any kind of ability to prevent or recover from fraud or simple mistakes.
Perhaps you can build a similar electronic system, but if one of the purposes is to make it slow and make it involve lots of manual confirmations, is there really a purpose to it? It's going to be much more complex than the paper system (replacing physical properties like uniqueness with brittle/complex cryptographic versions). Complexity always begets bugs.
