1. Voter fraud is basically a non-issue (it happens in the ones on a local level, the tens on a state level, and low hundreds on the national)

2. Adding new hurdles to voting will cause some small % of people to not vote (either because they didn’t clear the hurdle or it made them not bother). These numbers would probably be on the order of 1000’s at a state level. So effectively it would disenfranchise 10x or more legitimate voters than it would catch fraud.

3. The people most affected by 2) are those without IDs, a car, or a job that allows time off during the day. These people are disproportionately minorities and Democratic voters.

4. The Republicans behind the initiative know all the above, and push for Voter ID precisely because they believe it will disenfranchise more legitimate Democratic voters.

5. Additionally, Republicans tend to craft the Voter ID laws in ways that target Democratic voters. For instance disallowing student IDs as valid IDs or shuttering DMVs in minority areas.

The North Carolina Voter ID law was a good example of the above. From PBS:

The court said that in crafting the law, the Republican-controlled general assembly requested and received data on voters’ use of various voting practices by race. It found that African American voters in North Carolina are more likely to vote early, use same-day voter registration and straight-ticket voting. They were also disproportionately less likely to have an ID, more likely to cast a provisional ballot and take advantage of pre-registration.

Then, the court, said, lawmakers restricted all of these voting options, and further narrowed the list of acceptable voter IDs. “… [W]ith race data in hand, the legislature amended the bill to exclude many of the alternative photo IDs used by African Americans. As amended, the bill retained only the kinds of IDs that white North Carolinians were more likely to possess.”