You're right it's a very obvious thing that you should have to show your government issued ID to verify who you are to a civic function, and that relying on the honor system is something that seems like it could never work because elections are serious and people have vested interest in particular outcomes and so would obviously look to cheat.

But this is what I'm talking about it being a theoretical problem. It's so obvious that this could be an issue but it's not an actual issue and the USA stands as an example that, counterintuitively, you actually can rely on the honor system. And so because the system currently works as it is and there's no real problem to point to I think it is reasonable to be inherently suspicious of the motives of a government that wants to make a thing harder without being able to point to a concrete problem.

A less controversial example on hacker news would be having to show your government ID to access porn. We are all rightfully suspicious of the motives of a government that wants that when to most Americans it is plainly obvious that there is not a real problem being solved. It's so obvious that you should have to show proof that you're 18 in order to access 18 and up material but we have more than two decades of proof that just asking them if they're 18 and up works well enough.

I think you’re making the mistake of assuming that this thing that we can’t really verify (because we can’t make sure <person voting> = <person registered> at the polls) isn’t happening, precisely because we can’t accurately verify it. It’s not a theoretical concern that voter rolls can be stale (because of not removing dead people or people who have moved in a timely manner) or otherwise inaccurate. And attempts to actually purge voter rolls always meet stiff resistance as some nefarious ploy to disenfranchise voters. There is at any time a non-zero chance that you could vote using the name of someone who’s either dead or not around any more. So why so much resistance to safeguarding against that? Nevermind the added benefit that a national ID card could be used as a real replacement for Social Security numbers. But again, so much resistance to something that every other country thinks is a good idea. Which is even more assuming since we point to “well everyone else does it that way” for so many issues. But voter ID? Oh, well that’s complicated, couldn’t possibly work here.