There is a simple experiment you can do to test this yourself. Just attempt to board a US domestic flight without showing any personal identification. You will most certainly not be allowed through security.
Yes you will be.
I did it. Me. Personally.
If you show up at the airport and your wallet is 200 miles away and your flight is in 45 minutes they will, unquestionably, irrefutably, let you onto your flight.
Step 1: Go to the counter and tell them you don't have your ID.
Step 2: They typey-type on their computer and print out some stuff.
Step 3: You take that stuff to TSA and they ask you some questions like "what is your address? what is your date of birth? and things like that"
Step 4: They wave you through and you go to your gate and wait to board.
I was told that it is not uncommon for people to forget or lose their IDs.
Further validated by https://www.tsa.gov/travel/security-screening/identification....
I find it pretty funny that the top of the website says "Adult passengers 18 and older must show valid identification at the airport checkpoint in order to travel." Yet later in the page it says you can still travel without it.