I just got back from Washington DC. At no point during my journey did I have a government issued ID on hand. This seems to be incontrovertible proof that you can indeed fly without a government issued ID.
Now, by “no government issued ID”, I do not mean “presented a social security card, along with several non-government photo IDS.
As Bob Marley once sang, “hey mister police officer, I ain’t got no birth certificate right here.”
Flying to and from Washington DC, I only showed one form ID: my checkcard, which has my picture on it. I prepared an array of various papers, IDS, and whatnots to prove my identity, but no one ever seemed to interested in looking at anything more than my bank of America card.
