Omar Mateen was investigated by the FBI for links to terrorist groups. Yet when he went to legally purchase a gun it didn't trigger any bells to suggest he might be worth watching closely in the following days.
Fights over 2nd Ammendment Rights and gun control seem doomed to fail, but notifying the FBI of gun purchases and running those checks through a system to trigger an alert seems like a reasonable approach to try and catch someone meaning to do harm before they have a chance.