I think of it as another step in a leaky conversion pipeline, but instead of minimizing the dropoff the pipeline is optimized for maximizing. It's not that people are unable to fill 10 field form that sometimes randomly loses all your input, but more people will complete the form if it doesn't.

Another thing is when the id requirement is not just there, but added right before the election, so it's not "going to dmv once every 10 years", but "going to dmv this year especially so you can vote.

If I would be optimizing for the minimal dropoff, the policy would look like "passing the law that takes effect in 5 years from now, tasking the blah blah agency with increasing the id coverage and putting reminders how important it is to get an id and vote everywhere you look at, increased funding for the dmv and whatever". But no, it's has to be done with the urgency and framed as threat.

So the actual argument is not that there is link between race and going to dmv once in 10 years, but that the intent behind passing such laws is not increasing integrity, but favoring a specific party. Even if doesn't actually work, it's still one of the worst things a party in a democratic system can do.