Currently, there are many (>> 10,000 per national election) documented cases of voter disenfranchisement, and almost no (single digit, per national election) documented cases of fraudulent voting.

The voter ID laws make voter disenfranchisement easier and fraudulent voting harder, so they greatly increase the total number of incorrectly cast / denied ballots per election. Therefore, they do a small, bounded, amount of good, and a large, unbounded, amount of harm.