He wasn't convicted of a felony, nor misdemeanor DV, nor under a restraining order. All of which would have been disabling. His GF chose not to get one on him. Apparently his family knew he had mental health issues, and the FBI was aware of him, but no one bothered to use existing law to get him adjudicated mentally ill either.

If we aren't going to use existing laws, it's a bit asinine to call for more.

As for TSA / airlines checking: no, they don't, and no, they shouldn't.  You don't make major, expensive policy changes due to one incident, particularly when that incident wouldn't be affected by the policy change.