Today I just got back from a trip to the East Coast. I flew both ways, and never showed ID. I thought I'd report on my experience.
First, flying without showing ID is apparently easy, if you know the trick. When you check in and they ask for photo ID, just say "I'll be flying as a selectee today." This is an exception to the photo ID requirement (usually for folks who've lost or forgotten their ID, but they don't check). If you ask about selectee stuff, they'll deny it, but if you already know the game, it seems you can take advantage of it quite easily.
Apparently the clerks are quite used to it; I never even got a funny look. (Just a brief question -- "you forget your ID?" -- "yup.")
The huge downside is that they'll call a security guard to come hand-check your bags. The searches seem to be very perfunctory (never looked at my laptop, never noticed the bulky electric shaver I put between layers of clothes to prevent it from getting banged around). Also, the security precautions are terrible -- once you have your bags searched, you get your boarding pass, and are free to wander around until boarding, so I could easily have put my bags in a locker, checked in, retrieved my bags, and walked on the plane. (I wonder if doing that to avoid a search would be illegal.)
Still, I consider a hand search better than a ID requirement (especially when I know that it's coming, and am not carrying anything sensitive). The hand search results aren't tied into some huge computer database; the ID is.
Be warned that the airline is apparently not required to carry you when you fly as a selectee, and if you act even slightly suspiciously, I would expect them to turn you down. I flew clean-shaven, in a Princeton shirt, and was polite to a point; I'm sure that helped. Don't do anything to attract a manager; they're more likely to be suspicious, I think.
So far, I've only tried it twice, so I don't know how reliable it is. Have a backup plan. (Remember, there are several places you can check in, and they probably don't communicate. Also, consider carrying ID just in case.)
I checked in at the gate both times, because I didn't have any baggage to check. I'm told that you can still fly selectee if you have checked baggage -- and they don't hand-search your baggage -- but I think they will probably do positive bag matching. (A good way to make sure your bags are the last ones on the plane and thus the first ones off, so you can leave the destination airport as fast as possible!)
I flew on tickets purchased with a check. It says so on the ticket. I don't know whether they took that into consideration; I will try flying selectee with a ticket purchased in cash in the future.