American schools use cameras to look into crimes. They are not generally accessible immediately by teachers, but many British schools now have very elaborate camera systems designed for immediate use. When two kids get into a fight there is little debate about who started it. Teachers can, within minutes, have the footage on a tablet at their desk. Having that unbiased video evidence immediately at hand radically changes bullying prevention. Some kids and most parents may not like cameras, but that kid who is afraid for his or her physical safety wants those cameras working.
Microphones are a more sensitive issue, but I could see them being equally effective in addressing harassment. They would need different protections, perhaps a 30min recording limit, but there is potential.