But the legal dispute should not distract anyone from recognizing the underlying purpose of laws like these and their close relative, voter ID laws. They are intended to keep eligible voters from the polls.

Republican lawmakers who work to impose higher bars to voting — either through proof-of-citizenship or voter ID laws — are well aware that many of those otherwise-eligible voters who struggle to come up with the required documents, which include a birth certificate, passport or driver’s license, are more likely to vote Democratic. Sometimes they even say it out loud, as Mike Turzai, the majority leader in the Pennsylvania statehouse, did in 2012 when he bragged that the state’s voter ID law was going to “allow Governor Romney to win the state of Pennsylvania.”

In recent months, it seemed that judges were beginning to see through the pretense of such laws, whose proponents insist they are necessary to protect “election integrity” despite the lack of any significant evidence that voter fraud of any kind exists.

In reality, as Judge Richard Posner of the United States Court of Appeals for the Seventh Circuit wrote last year about voter ID efforts, these laws are “now widely regarded as a means of voter suppression rather than of fraud prevention.”

Nevertheless, Judge Melgren accepted at face value the claim by Kansas and Arizona that only “concrete proof of citizenship” can allow them to determine whether a voter is eligible. He ignored the fact that neither state had actually demonstrated that such proof was “necessary” to prevent fraud. Kansas officials identified at most 21 noncitizens who had registered to vote, out of more than 1.76 million registered voters in the state. The percentage of noncitizens alleged by Arizona to have registered improperly was similarly minuscule.