You have to prove residency in that state as well. This would mean a utility bill or voter registration, most likely. If you live completely off the grid and don't vote, you could probably not get a state ID in some states.

The US issues passport cards you can stick in your wallet, as well as the books. I carry mine because my state ID isn't "REAL ID" compliant, which is amazingly a thing that starts to matter before my ID expires.

Financial documents (eg: bank or credit card statements, loan documents, tax filings) with your name and street address on them are also a valid form of demonstrating residency in most (all?) states.