Seems reasonable to me. I'd lean toward a check on both, but at least we'd be consistent doing it for both or neither. There are probably other things we could throw in here that we currently check or don't check for as long as we're trying to be consistent across the board.
Interestingly aside from some loony activists I don't think too many rank and file Dems mind ID's for voting either. Any law like this should go into effect in time for the election after the next one coming up, so as to give people time to adjust. We can argue the merits or lack thereof for the GOP all day, but on this issue I think they badly mishandled it. The public by and large agrees with their stance, but when you have people passing laws and then going to the press and saying how you just guaranteed a victory for your party's Presidential candidate the public smells a rat.