I worry that all a private screening does is make it so that the rest of the public doesn't see what the TSA is doing.
I agree. I'm all for doing what we can to grind the checkpoint to a snail's pace as a form of civil disobedience. But, I think the stakes are higher with the gropings/pat-downs. We've got to do everything we can to keep this in the public's eye. If we take it to a back room, it will go away and the TSA will have won and the Constitution will have lost.
Once, when I was asked if I wanted a private screening, my response to the screener was, "Let's do it right out here in front of everyone. What are you afraid of???"