I once left my license on a photocopier in my home office just before leaving for a cross-country trip. It was perfectly safe, I knew where it was, but I didn't have it.

My departure point was Worcester, Mass. (ORH). I got into a discussion with the counter agent, she had my credit card (to confirm the e-ticket) and AA PLT (at the time) card, and never asked for a photo ID.

Returning from SFO with a colleague, we checked in at the Admirals Club. They saw my membership card and PLT card when I came in. We had a long discussion about availability of "sticker" upgrades for the two of us. (There was one seat available, so we decided to stay together in economy.) They also never got around to asking for a photo ID.

Pure luck, of course. I doubt that would happen at either end today, let alone both.

Even then, I wouldn't have recommended it as a standard travel procedure.