Requiring an ID only eliminates half the voter fraud issue.
The other is election workers at the polling places themselves. Even with the ID requirement, they can cast hundreds of votes themselves at the poll with essentially nothing to prevent it, no real way to prosecute, and no way to remove the votes even if the votes they cast were for dead voters as there is no manner to know who those votes were for.
The greatest election fraud is not by disqualifed voters voting nor people voting more than once coming to polls. It is the poll workers themselves.
I was an election judge at a poll in the past. I could have easy cast at least 100 votes if I was so inclined. Just vote 100 times and falsify 100 signatures. Even if it proven those signatures false, they couldn't prove I did it nor any manner to figure out which of the 100 votes to erase as there is no linkage of votes cast to the voter.
In some counties, that is so common that Republicans and Democrats negotiate - "you turn in one precinct and we'll turn in one precinct" back and forth so neither side can know how many votes to add for their side in tight elections. There have been precincts that have turned in more votes than all registered voters in the precinct. It really is simple. The election workers - partisan picked for most jurisdictions, just keep casting more votes. Since they are the polling place "cops", there is nothing to stop it.
My practice as election judge? I allowed anyone to vote. I'd remember if someone came in more than once. Election fraud so common, I felt mine still the most "accurate" because I didn't cast votes myself nor allow such fake votes cast by anyone. But I didn't challenge anyone either, whether or not they had a voter registration card. Even if not on the voter list I had, those are so screwed up it didn't matter. I just filled out a lost-card form for the person and gave the person a ballot after he/she signed in.
The only thing that would truly stop voter fraud would be to use biometrics and electronic voter machines (unique thumb print - only I ballot per.) Hard copy paper print out after each vote would address computer manipulation for the most part as the other problem.
I have no problem with requiring an ID, though I do understand the problem with it and why Democrats would object. Both sides have valid points. But that is NOT the main source of election fraud. Its the poll workers themselves.