The proven negative impact of the voter id laws, as far as I know, is very small. Michigan had .3% non-id voters, and Texas had ~.01% non-id voters. Both states allow voters to fill out an affidavit. These stats were just found offhand, I'm not sure if there's a comprehensive review.

So we have a small proven negative impact on democracy from voter id laws, and a small unproven negative impact from their absence; I don't think it's unreasonable to prevent a crime that is easily preventable under those circumstances.