But it still makes no sense to me to have rules about who can vote in federal elections without any mechanism to enforce those rules.

Thanks for taking the time to write out a reasoned reply.

However, I think your analysis is faulty. Often in law, lawyers discuss ex post regulations and ex ante regulations.

Sending people to jail who vote illegally is an ex post regulation. After you do something illegal, you get punished (and hypothetically, this deters others). Voter ID is ex ante; we regulate the attempt to behave illegally before it happens. Just because one doesn't support ex ante voter ID laws doesn't mean one doesn't support ex post regulations like criminal prosecution. I think adding this distinction to your analysis might change its conclusion.

Depending on the magnitude of the harm, you might want to regulate it ex ante rather than ex post. If a gun falls into the wrong hands, someone could die. Big deal. We shouldn't wait until that happens before we regulate. Therefore, ex ante regulation is probably a better fit. Moreover, there are a lot of criminals in america who want guns to help their illegal businesses or to act on violent impulses. So given the amount of people who want to act illegally with guns and the risk, ex ante regulation makes sense.

I'm not sure we could say the same about the number of people who want to vote illegally and the magnitude of the risk if that small number of people did vote illegally, no? Hence, ex ante regulation for guns, but ex post regulation for illegal voting.