If the TSA wanted copies of our ID's they could just put a bar code scanner next to the blue light under the counter and be like some hotels do, scan the code on the back of your license. They get all the info on the front in a split second, the person who handed them the ID doesn't even know it was copied.
They don't need to run to a photocopy machine.
Granted not all state issued ID's have barcodes, but many do, and a reader is dirt cheap.