How on earth does something like this get into the law.

Because Arizona wanted to find a way around the National Voter Registration Act ("NRVA"), also known as the "Motor Voter" law.

Back in the day, Arizona adopted a set of laws that would require anyone registering to vote to have to provide proof of citizenship. A number of groups challenged the law on a few grounds, but primarily that it violated the NRVA. Basically, the NRVA establishes a form for registering for elections, and the argument went that a state can't add to that form.

Went to the Supreme Court, and Arizona lost 7-2. Can't add requirements that are inconsistent with the NVRA:

en.wikipedia.org - Arizona v.

So they had a great idea. The NRVA can regulate federal matters, but Arizona can still regulate registration for state and local elections. So they amended their election laws to create two types of voter registration - a basket of voters that get registered for all elections (federal, state and local), and a second basket of voters that are "federal-only" - and imposed the extra documentation requirement only on the first basket. Which is most voters, but essentially trying to avoid the NRVA statutes by having this separate "federal only" bucket that doesn't require additional paperwork (but which is still a crime to vote if you're not a citizen).

Albaby