You are being disingenuous, Mike. The Driver's license is a matter of law for drivers, though it's not written in a document that predates the automobile.
Police may still ask for it. There may be some quarrel still in the works as to whether you actually have to show it when you're being stopped by police in a driving situation, but it's probably a good idea. You are required to state your name to a police officer when the officer asks you.
It would probably help speed things along if you show them some sort of identification as well.
The Arizona driver's license and their ID card apparently have data on them that say where you were born. I find that provision offensive, personally, and that alone would prejudice me against wishing to live in Arizona under most circumstances, at least at present. I believe the state is showing a lax attitude toward their civil liberties. My understanding is that you favor such states, however, and there is no accounting for taste.
Many states feel that such information is private and should not appear on such documents, and in their wisdom or, as you might put it, their folly, they have elected to maintain the privacy of their citizens. Arizona does not yet have the power to force other states to follow Arizona state law on the documents issued by those other states, much as you might wish otherwise. It does not have the power under the constitution to do so. The constitution suggests that each state may make its own state laws, and that quarrels between the states should be settled by the Federal government. Custom has settled that power on the Supreme court.
Thus, Arizona does not have the power to force other states to issue ID papers which satisfy the citizens and officials of Arizona and not the citizens and officials of the states in which those citizens reside, and of which they are, to be somewhat redundant, citizens. Should such papers be legal within Arizona for citizens of Arizona by Arizona law, that doesn't mean they are legal otherwise. Nor does that actually mean that the law has been well tested as valid and constitutional for use in any state.
You might check out some of the bases on which the law looks like it'll be contested. I'm not expecting you to agree with them, though you may. I simply find it intellectually interesting and you might as well.