Saying that there is “no legal requirement to show an ID” is truthy but misleading. Federal law gives the TSA authority over “screening” passengers: https://www.law.cornell.edu/uscode/text/49/44901 (“The Administrator of the Transportation Security Administration shall provide for the screening of all passengers and property, including United States mail, cargo, carry-on and checked baggage, and other articles, that will be carried aboard a passenger aircraft operated by an air carrier or foreign air carrier in air transportation or intrastate air transportation.”).

That means the TSA can do whatever it can get away with labeling “screening.” It doesn’t matter that Congress didn’t specifically require showing IDs. That’s just one possible way of doing “screening.” Under the statute, the TSA is not required to do screening any particular way.