And more: the argument consists of digging deeper and asking why, in the past decade, such a sudden, incredible, apocalyptically urgent need has arisen for in-person checks at polling places, with no equivalent need for ID checks with absentee/mail-in ballots.
Fraud with mail-in ballots would be orders of magnitude easier to pull off. Why don't states with draconian polling-place ID laws also have draconian ID laws for mailed-in ballots? Why, in those states, don't you need to bring multiple proofs of identity, residence and citizenship to a notary to stamp your ballot in triplicate before mailing it in? If fraud really was what they were worried about, they'd be consistent across these types of ballots. They aren't.
Also it's worth looking into the whole package of policies that usually comes with these rules. It's not just ID rules; it's a particular kind of ID, and a particular set of paperwork requirements, and closing down ID-issuance offices in certain locations, and closing down polling places in certain locations, and reducing hours for voting at the locations that remain open, and... well, let's just say meditate on that and you'll figure out what "problem" is being solved. If you're still not convinced, just go read the defenders of these policies, in their own words, in court filings, explaining why they're doing this.
Voting is fundamental enough that it should only be restricted in the event of pressing, urgent, demonstrated, proven issues, and only the absolute minimum restrictions should be put in place. Voter ID doesn't "solve" any such issue, and is not the minimum necessary restriction in any event (there are already mechanisms for challenging suspected fraudulent voting, if you're truly worried about that).