> 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.)

Note that drivers licenses wouldn't count as proof of citizenship under the SAVE act.

>but most states do not have a per se ID

Out of curiosity, do you have a source or list for this? My own home state and those around me that I've spot checked all have a state ID available as an alternative to a driver's license. My understanding was that this is the case for most states.

Unless I've misunderstood you and you meant a state ID that is completely separate from a driver's license to the point that people with a DL would have one?