Well, there are states that require a thumbprint to get a drivers license, so obviously it is an option. Of course, the real issue involves in part the question of whether we really believe that voter fraud is a significant problem. Again, I just cannot imagine that there are a significant number of people (if any) who would go to a lot of trouble to cast an extra illegal vote. In my entire life, I've never met one and in my entire life, I've never met anyone else who told me that they met one.
Common sense tells me that there's a reason for that.