This does not address any of the issues that people complain about? How do you stop somebody other than the person who is supposed to vote from voting using the person's ballot and faking the signature? Or a person could sign the envelope and give their ballot and envelope to somebody else to vote.
The point of voting with an id is to look at the picture and compare with the person to confirm they are the actual person.
edit: before you say they check the signature. It is not reliable. I know people who have had to confirm their signature despite it looking close. I've scribbled my name not even close to what I had recorded and it worked fine.