Sorry Forbes, but public safety is not one of those things that free market economics has any chance of doing better than government standardized or government run schemes.
It'd be almost an exact parallel of health care in the US. An organization responsible for something generally considered in the public interest, but with motivations other than, and sometimes in direct conflict with, that public interest.
As far as grievous things done by the TSA .. yeah, they are grievous and demand changes to only perform functions that directly relate to security.
As far as the specific example .. it's unfortunate, but as soon as TSA says they won't examine women who have had mastectomy is the day certain nefarious organizations start recruiting women who have had a mastectomy to take a defacto one way flight somewhere.