Investigators have yet to issue their final report on a Southwest Airlines Co. flight last month that ended in an emergency landing and a passenger’s death. But one thing is clear: Despite a warning about a suspect engine part nearly two years earlier, investigators didn’t mandate enhanced inspections for an unusually long time and acted only after the high-profile fatality.

Questions about the time it took regulators to mandate more comprehensive inspections—and whether an alternate response would have made a difference in...