Earlier quoted context omitted.
You could remove the TSA and let airlines do their own security checks at the gate. Airlines really don't want their planes hi-jacked.
I don't think anyone would be happy with 'British Airways Counter-Terrorism and Intelligence Services, plc.' and friends running surveillance, SIGINT and other spy operations to gather threat intelligence. And, unfortunately, it seems like intelligence-led prevention is the only real way to stop terrorism, detection and attempts at interdiction close to the target are going to fail the same way the TSA fails, due to…
I wouldn't expect British Airways to do its own SIGINT but there's no reason why it can't source that info from the current supplier. (And BA already collects the passenger info on the US government's behalf.)
Either way, no one is proposing to tear up the Do Not Fly list, risibly inaccurate as it might be.