I wonder, how exactly would the TSA have prevented 9/11? So far as I can remember none of the previous airport security missed anything that was banned at that time. Also, even if we presume that the TSA is 100% successful at preventing harm in an airport or on an airplane what is there to stop today's terrorists from shooting up our schools, our theaters, our universities, our shops, and our offices? Just curious how the pro-TSA side sees this.
And the Lockerbie bombers, I believe, checked their bomb in luggage of the American fiancee of one of the evil-doers. He was quite willing to sacrifice the love of his life to take out certain individuals on the plane (I've heard that some US government agents traveling on the flight were the specific targets). So, yes, the point is EXACTLY that someone might have been able to slip a bomb into the personal effects of the three-year old. And unless the TSA checks out carefully any "hits" that their detection system gets on the initial searches, then there is no safety.
The process could be done in an enclosed area away from the prying eyes of the general public, but it can (and should) be done.