I once read an account by a poll watcher of her experience in 2012. She said that at her polling place, there had been a number of people showing up to vote on Election Day, being told they had already voted during the early-voting process, and swearing up and down that that wasn't true, that they always voted on Election Day and never voted early, and that whoever had voted in their name had done so fraudulently.

Now, in that particular case, the state (I believe it was Colorado though I'd have to find the article I read, and I don't remember where to find it any more) didn't require photo ID, so there was no way to prove that the people showing up on Election Day were the actual voters, as opposed to the cheaters. But this poll watcher's opinion was that they were the actual voters, and the cheating had been done by whoever had submitted ballots in their name days (or weeks) earlier. Given how many people she said this had happened to, I'm inclined to agree with her: it wasn't three or four people, it was (she said) something like one-third of the people who showed up on Election Day at that polling place.

That's a case where the fraud couldn't be repaired by knowing that it had occurred — the fraudulent ballots (if they were indeed fraudulent) had already been accepted, and it was impossible to go pull the ballot allegedly belonging to Joe Smith back out of the ballot box. But the publicly-available list of "who voted" did at least make it possible for the fraud to be detected in that particular case.

Yet so few people go the next step and say, “Let’s do away with the secret ballot itself.” It really is a recent invention, American democracy survived nearly 100 years before the Australian ballot was adopted. There are obviously concerns (vote buying, organized crime, etc) but they can be dealt with. And public voting would almost completely eliminate concerns about the voting process itself being subverted by a malign actor.