They do, but those are mostly intended in case somehow all the lift cables snap/detach/disappear. In that case the elevator would drop, the brakes would engage

They do, but those are mostly intended in case somehow all the lift cables snap/detach/disappear. In that case the elevator would drop, the brakes would engage and slow the elevator down to a stop. In the story told you can easily imagine the elevator dropping and getting caught by the cables in a time frame shorter than what you'd need for the brakes to stop the elevator. A drop of just a foot could easily cause plenty of injuries. EDIT: I should also mention that the mechanism I described above should not be confused with the overspeed governor which is located in the penthouse and wouldn't notice anything at all if the lift cage gets stuck.