The FBI does not have a mandate to investigate all reported crimes. AFAIK, no law enforcement agency does. They triage the reports, and most reports don't get investigated.

Most mass shootings don't have a lot of the FBI to investigate. The perpetrator often dies on site, so they can't be charged with anything. FBI will likely investigate if there were any co-conspirators, and may work with ATF to determine how the perpetrator obtained the firearm(s). Many times we hear that the perpetrator was "on the FBI's radar", but most of the time, there was no unlawful conduct before the shooting, so what are they supposed to do?