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.
Voter ID laws are a non-starter because historically they've been used, along with literacy tests and civics tests, to disenfranchise people who can't get an ID. For example, in Idaho you must have "proof of your identity and age" like a birth certificate or citizenship certificate, plus proof of residency like a utility bill or rental agreement or employment record.
These things are easy for most people to provide, but people who are in unstable living situations may find these things impossible to provide. Requiring those people to provide ID at the polls would effectively disenfranchise them.