A soft iron core is useful when you want an electromagnet to switch off rapidly.
Some cranes use electromagnets to pick up scrap cars. They can let go of the car by turning off the current.
Electric bells use electromagnets. When the electromagnet has pulled the striker towards the gong, the current stops to let the striker move back away from the gong again. The current restarts and the movement of the striker continues. The circuit is constantly made and broken.
Electrically operated switches called relays also use electromagnets.