This would certainly seem to depend on what aspect of travel that one is thinking about (the "Soundproof Airport Motel" that used to be across Cicero Avenue from MDW comes to mind). Are you talking about paying cash and traveling with a Chicken Inspector badge?
In terms of being required to identify oneself,
Gilmore v. Ashcroft is still kicking around. Nothing new in PACER when I checked a week and a half ago, but as far as the airlines are concerned, if it's not law, it will become "policy," so I think you'd be stuck with carrying fake ID.