You CAN travel w/o ID
I've tried this three/four times in the past couple months and was surprised even with checking bags.
To sum-up:
Flying without ID is doable but will subject you to secondary and the "TSA massage".
If checking bags you will be asked by the airline for ID; not sure why but refusing (for whatever reason - lost it, choose not to show it...) will get you a reprinted BP with SSSS if you checked in at a kiosk.
If you are not checking bags, check-in at the kiosk, get your BP and head to the line. When asked for ID, refuse and get marked for SSSS.
The airports I've been through (DCA, SFO, LGA, JFK, MSP, EWR) have been removing you from the "normal" line and escorting you through, either ahead or through the elite lines (if present), with "specially marked" bins to designate them as containing SSSS-associated items (my guess).
Pass through the WTMD (with your shoes off - still haven't tried that one yet) and follow the TSA'er with your bins to the SSSS tables.
Be sure to insist on new gloves - I've done that each time w/o complaint from the TSA'er. Enjoy the massage and the rifling through your belongings while they're being swabbed for ETD.
In/out in about 15 minutes, depending upon how many swabs they insist on running through the machine (one took nearly 25 minutes and involved 5 or 6 swab tests).
All w/o showing your ID.
Better yet, when not showing ID there's little chance of them recording any personal information on you other than date, name, airline, & flight so there's less risk to your personal information if you decide to respond (what I would consider) appropriately to inane questioning.
Best of luck and I plan on continuing to do so whenever I fly alone. The Missus doesn't necessarily appreciate my libertarian streak while I'm at the airport...
Enjoy!
BF