One of voter ID's biggest advocates, the Heritage Foundation, could only find 68 cases of non-citizens voting since 1980. Even if all of them are repeat offenders, that's a few hundred bad ballots out of billions cast. As you said, it is also possible to catch these people. Our election integrity is not threatened by non-citizen voters. It just doesn't happen on the scale that Republicans insist it must be happening, and the fact that they keep repeating it doesn't make it true, it means that they have an agenda that benefits from making you think it's true.