@Roberta,
They have non-driver ID in other states too. To answer Vonny's question about the number of docs required, when I moved to NM I had to register my car and get a state driver's license.
I had my photo drivers license from California, but was also required to show my social security card, birth certificate, 2 utility bills and mortgage or rental docs with my NM address on them to prove I was indeed residing in the state and was a citizen.
Things tightened up after 9/11 and due to recent additional hurdles put in place to make it more difficult for immigrants, legal and otherwise, to settle and assimilate. Also slows the ability to comply with new voter ID laws that require a photo ID.