It’s not the corkscrew shape that lets springs snap back.
All materials, when bent, have a range of “elastic deformation” – in this range of motion they will return to their original shape. When you overshoot this, you either permanently bend or break something.
A solid metal bar will experience this too.
A coil allows a small bend in the metal to add up down the length of the spring to make a larger bend. This means that no individual point of the spring bends a lot, but they add together to bend a lot. They never bend so much to break or get permanently deformed.
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