In Minnesota, you show up at the polling place, say your name and address, they find you on the registration list, check you off, and hand you a ballot. No need to prove you are who you say you are. If someone pretends to be you before you vote, then it's immediately and obviously brought to the attention of the judges (and we aren't seeing a massive wave of fakery now). If someone pretended to be you after you vote, they'd get caught.
Of course, someone could fake it, with someone's registration that they know won't vote. But if they repeated it at a single precinct, the odds of being recognized as a repeat voter by the election judges goes up. So they would have to move from precinct to precinct, with a list of viable registered non-voters to use.
Now, consider scale. A statewide Minnesota election is about 1.5M voters. To move the outcome 1% requires 15,000 votes. If one person can manage to vote illegally ten times in a day, it would require 1500 people in a conspiracy. Plus data management, tight enough for no errors. And NO leaks while these 1500 people are trained (and probably paid, if you want that many).
With that in mind, the idea of actually manipulating the election with votes that could be prevented with Voter ID is absurd. But! If we put ID laws in place, we could well reduce the number of voters by 1%, and that result would be biased toward people who are poor or otherwise not fully integrated into mainstream society.
Election manipulation, completely legal, and more effective than the mechanism it purports to prevent. Ugh.
And hey, if voters are dumb enough to fall for that, maybe we can get them excited for touchscreen machines!