Airlines want to deliver passengers to their destinations. If they fail to do that, they lose passengers and revenue, and go broke.
Seems to me that an airline would have a strong incentive to ensure passengers arrive safely. It could be argued that the Lockerbie bombing led to PanAm going out of business. It may still be the case that TWA suffered the same fate.
Rather than have an over-weening bureaucracy decide who can fly, and who cannot, why not leave it to the airlines? They have far more incentive to get it right than TSA bureaucrats. Under the current regime, if a plane goes down, the bureaucracy imposes tougher rules on the American people, as if Americans were Jihadists. Under an airline centric system, no threat would make it on the plane.