I think at this point as a practical matter, the federal government is too deeply involved in airport "security" to cede control to the airlines. Even if TSA were to be disbanded, the feds would still control what private contractors were required to do at the airports, which could just lead to greater abuses/incompetence. I don't think there is much point in getting rid of TSA, better to somehow change the culture at TSA.

If I were in charge I would move TSA from DHS to the Department of Transportation. I would shift screening priorities to cargo and go back to pre 9/11 levels for passengers. I would also let go of all but the few professional TSOs, raise pay levels for TSOs, and hire some new TSOs (although far less than are currently employed) who are capable and have a security background---and thus have a leaner but skilled workforce.