I would change the voting laws to force everyone to show up in person to sign up and show up at least once every four years and show proof of identity and address to stay on the voter rolls. If you can't find five minutes once every FOUR YEARS, you probably are too busy to know what you are voting on anyway.
I've had to show proof of identity before. I think it was the first time I voted. Anyway, I ALWAYS take my ID in with me so I have it if asked. I live in small town Iowa, so, they all know me and never ask for it!! But I like your idea A LOT!!