ID is only necessary if you haven't already established the right to vote in a particular location. After that, you're on the list and it's remarkably difficult to get you off of it; as it should be.
ID requirements are frequently used in order to deny voting to people who are poor or otherwise find it difficult to get particular documents.
With paper ballots how do we guarantee those with a right to vote who cannot travel to a secure voting location have the ability to do so?