Frankly I think that level of restriction if bullcrap when applied to what is a plainly written right but this level of restriction is applied piecemeal to various rights by various states both at present and in the recent past. Legislatures does not see things as plainly as you or I do. They deal in these kinds of mental gymnastics as a routine part of their business. Just because something's obviously incompatible with the constitution doesn't mean it can't be the law of the land (especially at a state level) for a generation or three.
As an aside, an ID is typically required for all sorts of things that poor people do a hell of a lot more than rich people (change jobs, use a check cashing service, sell scrap metal, sign a lease on a new apartment, register a car, apply for .gov assistance, interact with the government in general, etc.) so they do tend to treat acquiring/renewing IDs with more urgency than the HN crowd because not doing so will cause them problems in shorter order.