It feels like you're suggesting the reality of voter ID in the US isn't how I'm describing it.
In the US, there is no national ID card. The de facto ID is the driver's license, and those are issued by the individual states -- and for people who don't drive (which, in most places in the US, means "poor people") there's no reason to have one.
States DO issue a non-DL ID, but getting one involves a bunch of the same hassles that getting the driver's license involves -- paying a fee, taking time to go to the correct government office, taking time off work to do so (again, a large imposition for lower income non-drivers), etc.
The GOP is also infamous for reducing polling places in areas that tend to vote Democratic, and really only gets in trouble when they're super obvious about it. Now, with VoterID, many GOP-run states have also starting closing the driver's license issuing offices in poorer and blacker areas of the state (for example, Alabama). There, you get a snowballing effect: reduce polling places easily accessed by poorer people; require an ID to vote that many of them don't have; and then make it harder to GET the ID in order to vote.
This is the new American reality.