Would the TSA cavity search every single passenger in order to safe 1 human life?

And would such a violation be worth the single life? Imagine the trauma that rape victims would have to go through, after being told they have no choice but to have someone search inside their bodies. They would be stunned by fear into compliance, so don't think that every single one of them would turn and leave the airport (because they could be fined if they do, as the TSA claims to have the right to.)