I'm sorry. I didn't make this clear enough. I thought "voter registration was an innovation of the Progressive Era" spelled this out, and that it was sort of also implied by the fact that for much of the 19th century, we didn't even have widespread photography, and certainly not photographic ID, but, to be clear: my point was that in the 19th century nobody had to go to the DMV to vote, because voter identification wasn't a thing.

Before I responded to your original comment, I did some poking around about 19th century voting practices. It's an interesting question. If you want to keep talking about it, can I ask first if you've taken the time to do the same thing? This is one of those discussions where we don't have to derive everything axiomatically.