There may be some potential for liability, if this was applied to facilities open to members of the general public. It's one thing to do it in a national-security facility, or apply this policy to employees, but it would be another thing to do it to random members of the public.
What if I enter a library or movie theater, decide I want to leave, and refuse to show ID on the way out? Are they going to physically bar me from leaving, under threat of violence? If so, that sounds a lot like false imprisonment -- a felony. It may also be battery (if they touch me) and/or assault (if they threaten me). On the other hand, if I decide to leave and they don't bar the path, then that's a big gaping loophole that raises questions about the purpose of "requiring" (but not really requiring) authentication on exit.