> It's not as if visibility into whether someone voted or not has driven voter turnout

Actually, it does. If the party you are registered with thinks are a voter who might not make it to the polls, and this is a close/important election, then there is a good chance you will receive numerous calls and/or visits reminding you to go out and vote. However, if you show up on the list of people who have voted by mail OR if you appear on the registry of people who have already voted in person, then they will stop reaching out to offer rides and reminders.