Depends on the disaster. Some stations do the weather disasters because they are predictable. Mass shootings aren't, and it takes time to get reporters to the site. There's usually a delay between when something happens and when we know about it. When the mass shooting hit Buffalo, three radio stations provided long form coverage. The reality is a music station isn't going to have qualified staff to handle a disaster, so they're better off staying with the format. You want to have someone qualified reporting on a story, not just a local DJ. Which is why most stations have deals with the local TV news team. Usually the local public station will be the most predictable for coverage, just because they have qualified staffing.
The FCC eliminated most of their news requirements in the 70s & 80s. So it's really not an FCC matter. The Minot train wreck in the early 2000s may be what you're talking about. There were congressional hearings. The disaster happened at 2AM Sunday morning. Local police and emergency staff called the main number of the radio station rather than the designated emergency number. Even then, the station was able to call in its news director who was on the air within an hour of the disaster. The congressional hearings concluded that the radio station was not at fault, and that the train should not have been traveling in a populated area without advance warning.