Helmets are absolutely necessary for caving and mining. They protect you from banging your head at the sometimes low ceiling and from falling rocks. They are even more important in mines, as they often have low ceilings, and the man made caverns are often unstable. In all show mine we know the visitors are provided helmets, just to give them the feeling to relive the miners life. In show caves normally no helmets are used, as only caves with a high ceiling are developed into show caves, and caves have formed during millions of years and reached a stable state when they are visited by man.
Helmets are very useful for cavers. They provide them from banging their head at the ceiling when they look for steps on the floor with low light. But even more important: caving light is normally mounted on the helmet, at the forehead. So the light always points in the direction of your head, which is the direction you're looking in. And you have both hands for climbing, no need to hold a lamp.