Nice theory. Unfortunately, you’re forgetting that only legal citizens can vote in U.S. elections.
And before you say “That’s why they wanna repeal voter ID laws”, I’ll say that you need to register to vote, and in order to register, you need to provide proof that you are a U.S. citizen, which is not necessarily a federal ID but could also be a SSN or a drivers permit (they’re not counted as federal IDs in some states)