But there have been 31 proven cases of voter impersonation in over 1 billion votes cast over a 15 year period. Meanwhile, the number of definite adult citizens who lack photo identification is in the millions.
Standing in line to fake a vote is time-consuming, requiring you to stand in line for possibly hours, you definitely can't do it more than once per person per polling station, it carries a risk of fines, jail time and being branded a felon for life. All for the sake of a single extra vote. Basically the effort and risk is so disproportionate to the reward that it's a non-existent crime.
Also, to "impersonate" a voter you do need to have memorized complete registration details for a registered voter, and be sure that they're not going to vote anywhere else. To get that level of specificity for thousands of votes would need a concerted effort with a massive database. It's not something you could just do on a whim because of the "lack of voter ID requirement". And if there really were thousands of fakes standing at every polling station: the amount of people required to pull something like this off and actually effect an election, then you can be sure they'd fuck it up quite often enough for there to be constant smoking guns and details that don't match up - plus the fact that each "fake voter" would need to have a unique properly-registered identity memorized for each fake vote they want to place at each polling station, and all of them would need to be careful not to slip up and mix up their details.
In any case, if you managed to fake enough voter registrations to skew an election, you wouldn't bother with a plan where hundreds of people march from polling station to polling station with stacks of fake voter registration details that they need to get correct each time. You'd just send postal votes. So the voter ID laws really are useless, because they protect from a non-existent crime that only an idiot would try, but would actually require genius-level planning and hundreds of accomplices.