This is about as possible as ending the war on drugs was in the 80's. Just because something is reasonable and makes sense doesn't mean it is possible to implement politically. In fact, I'd say an inverse relationship exists between common sense and what's implementable politically in the US. You simply face too much fear and stupidity.
I think "fear and stupidity" is overly simplistic. People overestimate how worthwhile it is to address low-probability, high-consequence threats. Everyone. I know plenty of rational people that rail about terrorism being a low-probability event who would freak out if they saw a pregnant woman have a glass of wine. Or saw a kid playing unattended at a playground. Or someone feeding a kid formula. Or GMOs. Or whatever--almost all of the highly educated people I know have one or more things that they believe to be risky that is not supportable based on hard evidence. It's universal.
Right now the wife and I are in the market for a new toddler-hauler. I want to buy two-years used, and ideally American, but I cannot get over the fact that only a handful of recent models, none American, get a "good" rating in the new IIHS small-offset crash tests. I know that a Ford made in 2015 is perfectly safe, but I'm going to spend a bunch more money on a new 2016 Honda because I'm irrational.
If you didn't have irrational fear, the TSA would not have its current powers. If you didn't have so much stupidity, the TSA might manage more than a 5% success rate. Yes, there are other elements like hate which also come into play here, but there certainly is no element of rational thought that goes into these types of laws. Yes, people have their biases and individual quirks, but it's certainly possibly to come up with and implement a system that doesn't simply pander to people's fears and plays on their stupidity. There's just no interest in such a system from either the people who are in control or the scared masses who are afraid of terrorism or other scaremongering tactics practiced by the former set of people.