> most states do not have a per se ID

I haven't researched this thoroughly, but what state will not issue an ID that is equivalent in every way to a driver's license except that it isn't a license to drive? I just checked Mississippi, Wyoming, South Dakota, and West Virginia, all of which do, so clearly being rural, poor, or both isn't enough to stop states from doing it. (The detailed politics are, as you say, a mess.)