I am a citizen of the United States of America, entitled to vote, buy alcohol (being over 21 by nearly four decades), etc., by the fact of having been born here. (Siege represents the other aspect, in that, while raised here, she was born in the U.K. and became naturalized.)
I do not need to prove that to anybody; it’s guaranteed me in the first clause of the Fourteenth Amendment to the Constitution.
If you can advance some valid reason why such a measure might be needed, then it might pass constitutional muster. The convenience of the TSA, police departments, and other functionaries, does not constitute sufficient reason to mandate one.
If you think there should be a standardized federal form for identificaiton issued by the states to people voluntarily seeking it, e.g., to certify their being licensed to operat a motor vehicle or their desire to have a valid state-issued form of identification to show bouncers, check cashers, etc., then propose just that – Federal DOT or someone to set up national standards and enable the states to conform their licenses to it.
But if you plan to require me to have one to vote, or to show to a cop when he takes a mind to stop me (presume me not to be operating a motor vehicle at this point), then you’re heading for a Statist state that I object strongly to.