Because along with that National ID law they can also setup a proper registration system, absentee voting system, and as such, do away with asinine 'voter suppression' schemes.
If done properly, there is literally no valid excuse any longer for someone to say their vote was "suppressed". The entire solution should take no longer than 4-6 months from high level case to detailed technical requirements. It is beyond sad this is even an issue in the US, we could be leading the world and showing - and providing - how it should be done, rather than being the joke we are. It's embarrassing...
Chuck