I'm under the impression that to vote you must register in a voting district, surely that registration requires something like a birth certificate or a SSN, which I believe is the only requirement for a government issued ID... Operating on the idea that the requirement for government IDs may in fact be a good faith measure to prevent voter fraud, would perhaps an optimal solution be to bring a web camera to that voting registration area and simultaneously issue IDs there?
To be honest, I thought it was a non-issue since my voter registration is also my draft registration, so I assume I provided some form of citizenship proof when I registered. It was a while ago though so I don't recall the details.
[1] https://www.atlasobscura.com/articles/election-fraud-in-the-...