My only beef with your above statement is calling the violations unsubstantiated. They are substantiated.
But yes I agree they do have a principled and an underhanded reason for pushing for those laws, just like Democrats have a principled and an underhanded reason for opposing them.
Where have they been substantiated? Check this out:
http://www.nytimes.com/2007/04/12/washington/12fraud.htm
You may find rare instances of actual voter fraud, but they are exceedingly rare. Conversely, studies have shown that voter ID laws will actually disenfranchise legitimate voters. In my view, the exceedingly rare cases of voter fraud that may or may not be detected through voter ID laws are an insufficient basis for disenfranchising any legitimate voter.